Even if that was true… how much more productive do you think learning to touch type would make me? And why?

Factually untrue.

My keyboard changes somewhat every time I buy a new laptop or have to sit down in front of someone else's machine for a while, eg a pool machine at uni. Especially the UK/US thing. Or use my phone and its various virtual keyboards. My daughter has just acquired one of the older MacBooks with a soft/programmable bar at the top. That changes dynamically. Would have broken my use of one of the few keys I do 'touch' type with muscle memory: ESC for vi, so I skipped that round of Macs.

Please don't make careless absolute or other very strong (wrong) statements if you want to have useful conversations without infuriating those who are careful with words.