Unfortunately at this scale, when you are this soft on the message, everyone ignores it and keeps doing what they were doing before. Carrot and stick are both required for performance management at this scale. You can argue whether the bet is worth it or not, but to even take the bet, you need a lot more than some resources and a "please".
It's not inevitable, it's just poor leadership. I've seen changes at large organizations take without being crudely pushed top-down and you'd better believe I've seen top-down initiatives fail, so "performance management" is neither necessary nor sufficient.
The executives pushing AI use everywhere aren’t basing it on actual performance (which is an orthogonal concept). It’s just the latest shiny bauble.
If everyone is ignoring it, it can't be that great. If it's that great, people will adopt it organically based on how it's useful for them.
If performance was the true goal then we'd just naturally see slow adopters unperform and phase out of that company. If you make good tooling available and it is significantly impactful the results will be extremely obvious - and, just speaking from a point of view of psychology, if the person next to you is able to do their job in half the time because they experimented with new tooling _and sees some personal benefit from it_ then you'll be curious and experiment too!
It might be that these companies don't care about actual performance or it might be that these companies are too cheap/poorly run to reward/incentivize actual performance gains but either way... the fault is on leadership.