You get good crosstalk performance by paying close attention to circuit layout. The mechanism by which crosstalk occurs is usually capacitive coupling. Imagine you have one wire running parallel to another. You drive a signal down the wire 1 and it induces a signal in wire 2. Hence the left leaks into the right or vice versa.

If you are highly concerned with crosstalk performance then you should ditch TRS headphone jacks altogether. The mechanism is different from capacitive coupling that you see on a PCB for example. The resistance from the common ground will induce a fair bit of crosstalk. I'd expect it to be the amp's dominating factor w.r.t. the crosstalk figure, but don't quote me on that as there's probably some very poorly laid out circuits out there. It's so ridiculous that I've seen cleaning a headphone TRS jack with isopropyl improve the crosstalk figure by 10-20dB. Again, that additional contact resistance that is shared by both channels is enough to make a difference there. The issue also gets worse with low-impedance loads, as they draw more current relatively and induce more signal in the other channel by extension. Take a very well laid out amplifier and unload the output then measure the crosstalk. Expect the crosstalk to be 50dB (!) or better with a 10k load rather than a 32 ohm load. With a TRS jack that is.

As to whether crosstalk really makes a difference...it's a bit like the distortion question. If you take .01% THD for a 100dB signal you'd certainly be able to hear the 20dB overtone alone. But whether you'd be able to hear it while the 100dB signal was playing...see for yourself. You can try the same thing for crosstalk with your headphones. Play your music in one channel at however loud you feel comfortable and pad the signal down 70dB or whatever and see if you can make it out in the other channel while it's playing. It's possible that you'd hear the image shift ever so slightly while the crosstalked signal is playing. But again, imagine a semi-correlated loud signal was also playing in that other channel above that ever so slight crosstalked sound. See for yourself if you're interested.

Crosstalk is certainly a nice spec to see but I can't say I've ever heard it as "easily audible". I do think many pyrates (myself among them) have certain amps/DACs that seemed to have smaller or more compressed soundstages, but I couldn't say how closely it relates to the crosstalk figure. At the end of the day you should put some more faith in your ears and listen to all your options and decide from there. Choosing audio gear based on a single spec is a major pitfall IMO.

Crosstalk is  only determined by capacitive coupling in very high impedance circuits.
It has no influence in low impedance circuits as a capacitance of even 100pF won't couple audio frequencies into 100 Ohm lines
At 20kHz a 100pF has a reactance of 80kOhm.
Into a 100 Ohm line that will give a channel separation of -118dB.

So the capacitance bit only explains crosstalk in high impedance circuits with signal paths extremely close together.
Think dual or quad opamps.

For HA with TRS sockets the real culprit lies in common ground resistance.
The lower the HP impedance the worse it gets.
It also differs in type of crosstalk from capacitive induced and this is easily measured using a scope and a sinewave signal.
If the phase differs its capacitive, if the phase is 180 degrees off it's a resistive problem in the common (ground/return) path.

If you want to test the audibility of resistive effects simply put a small 100 Ohm potmeter in the 'common' wire (sleeve of the TRS plug).
It changes the stereo image audibly with a few Ohm already.

This is NOT the same as output resistance of an amplifier b.t.w.

Even if you have an amplifier that has 200dB channel separation it is still completely pointless.
Why ?
Because the problem is the common return wire + the HP plug contact resistance + ground resistance in the amplifier.

The contact resistance is low in most cases but if you turn the plug inside the socket and hear scratching or intermittend sound it is already questionable and most likely measurable.
How is the 'returnpath' layed out in the amplifier ?
Is the TRS jack soldered onto a ground plane ? Is it connected with a short or even longer wire (rooky mistake for a lot of DIY amps) ?

These 2 may not give that much resistance so may only increase the crosstalk slightly.

The biggest problem is in the headphone cable itself IF it is a 3 wire cable that splits the returnpath IN the headphone itself.
Even a 0.1 Ohm returnpath wire with a 32 Ohm headphone will reduce an incredible measuring amp into a separation of just 50dB.

Solution ? Rewire the headphone and use a 4 wire cable and connect the returnpaths in the TRS jack only IF you only have a TRS jack.
Not that much of an issue with 300 Ohm HP's where the same cable resistance has a 70dB channel separation.

How audible is crosstalk ?
Remember the vinyl and cassette tapes... -30 to -40dB crosstalk was already a good value.
Hear any complaints about this from vinyl lovers ?

Some people even use crossfeed to 'improve' the perceived stereo image as most stereo recordings are made for speaker fi.
How much channel separation do you need for speakers when both ears hear both speakers ?
Sure... time domain, reflections, FR changes etc do have an affect.

Crossfeed lowers the channel separation for lower frequencies enormously (less so for higher frequencies) and some love it for headphones.
This is NOT the same as capacitive crosstalk though as is works the other way around in the frequency range (more crosstalk for lower frequencies in crossfeed).
Also it differs in resistive crosstalk as that widens the stereo image (a bit like the 'spatial' button on old stereos) where crossfeed narrows it.

Personally I don't give a crap about stereo separation at all if it is better than 40dB.
40dB is a LOT already.
I don't think it is an important number at all.
Most single sided entry headphones use 3 wire cable anyway completely F-ing the numbers up anyway.

I've never encountered a system where crosstalk was a noticeable problem.

Another source of cross talk is through the power supply. This gets worse as the load impedance gets lower. Drawing more current from the power supplies can cause them to be modulated at the audio rate.

I'm going to change the way I do cross talk measurements. Currently I do them without a load on the amp which delivers better numbers and may be more indicative of the capacitive/inductive crosstalk that happens in the audio circuits...but is likely less sensitive to crosstalk through the power supply. I'm going to change my routine eventually to measure crosstalk both loaded and unloaded.

Not sure how bad crosstalk figures are heard---in fact, the Auralic Taurus has a lot and is still a lovely sounding amp. (In that case I actually think it was intentional as they found it beneficial in subjective listening trials.) But in most case I think poor crosstalk figure would mostly be a measure of the designers prowess.

I'm going to change the way I do cross talk measurements. Currently I do them without a load on the amp which delivers better numbers and may be more indicative of the capacitive/inductive crosstalk that happens in the audio circuits...but is likely less sensitive to crosstalk through the power supply. I'm going to change my routine eventually to measure crosstalk both loaded and unloaded.

Just a tip when doing loaded crosstalk measurements.
Make sure the dummy load is connected directly to the TRS connector and connect the test leads to the TRS solderjoints as well so both the dummy load and test lead are connected to the exact same points on the TRS as close as possible to the amplifier.
When you have a piece of wire and then connect the dummy load to it and use test leads from that point you can get quite pessimistic values.

The headphone wires ARE the biggest culprits when a 3 wire HP cord is used where the return wires split in the headphone.
4 wire cables where the returnpaths ONLY connect in the TRS plug are optimal and just barely 'worse' than balanced (with a proper HA)

Also realise capactive, power supply and common return wire crosstalk are all crosstalk but manifest themselves differently.
Capacitive is the least worrying, power supply can be the most nasty one as the power rails currents are 'rectified' (half wave) currents that can produce nasty 'spikes' when a POOR LAYOUT or poor DESIGN is present.
It usually boils down to the ground plane (ore lack of) and signal/power supply layout problems which cannot be completely eliminated without redesigning the board.
Resistive (relatively high Ohmic common ground wire) will WIDEN the stereo effect (fuzzy-ing the center image) while the capacitive form works the other way but is usually inaudibly low.