Regarding ropes, for most practical applications I can think fro the top of my head, tensile strength is not actually that much of a limiting factor (especially with dyneema), but more the abrasion resistance and how easy it is to handle a rope.

I mean, you could in theory rappel from something like 2mm dyneema line with very comfortable safety margin on tensile strength alone, but 1. keeping a say 60m long 2mm line untangled is a serious headache, and I would not be comfortable holding my weight on the 2mm rope while letting it scratch against a rock wall .

if the load bearing core is miniscule and light you have plenty of mass and radius available for abrasion resistance, handling properties, etc ...

Yes, but we are there already in many applications where we need to pad the core for abrasion and handling. Making the core even more smaller makes no big benefit - unless it is substantially cheaper than the competition.

And to be clear, I believe there are multiple applications for higher tensile strength fibers. I just can't see that many applications where thinner ropes than current technology produces would be a game changer.

Depends on the use case, Zylon is one of the strongest fibers, and is used for rigging in competitive sailing. However it's not UV stable and not good with repetitive bending, so I'd not recommend it for climbing use either...

Manufacturing garottes? Like, maybe that fancy device in the movie "The Counsellor".