The wires on the switches and outlets of your house are also pressured welded.

Same basic concept, different level of force. The press applies something like 2 tons of pressure, a bit more than you're going to get from your average hand crimper.

Why do they look like they are using a fancy crimp press? Also doesn't cold welding require both materials to be the same and completely clean free of oxidation, coatings, gunk, crap, silver linings, sweat from mexican workers, etc.?

Cold welding needs a lot of pressure... not sure if that little hand press will actually do it. It's a small enough area, but I have doubts. Other factors that raise a flag: you want clean, flat & parallel, non-oxidized surfaces. I don't see any of that here.

A use of fluid/flux/unicorn tears might remove some oxidation or corrosion, but you still have to remove that gunk prior to welding.

Now a specially chosen filler material that lowers the melting point of the two contacting metals, that could potentially reduce the amount of pressure needed to bond the surfaces... but that's kinda like brazing. Usually this process also requires some heat to achieve diffusion bonding. A paste flux still has all the non-metal gunk in it which would interfere. A carefully controlled multistep pressure application that starts from the centre and expands outwards to push out the flux is a maybe, but again I don't see that happening with the one-step hand press.

If the metals being joined have a large difference in galvanic potential, magical fluid won't do much. Just about anything aluminum will ruin your day.

And technically you'd be better off with bare wire into the speaker terminal anyways, since any connector at minimum adds two interfaces 

I weld all my cables with enough pressure to cause neutron degeneracy.

fucking degenerates, they will tell you anything to sell cables...