You could mount the cooler directly on top of the die with the Athlon XP. Turns out people kept damaging the CPU, hence the switch back to heatspreaders.

Permanently attaching a cooler to the CPU itself doesn't really seem like a viable option to me. Mounting it to the motherboard would be a nightmare, and you'd end up creating a one-size-fits-nobody cooling solution. Nobody would be happy with the cooler you end up choosing.

In reality, cooling paste really isn't that big of a deal.

This one does[1]. It have a bunch of pistons on springs touching each chiplet, all in mineral oil. Price bit out of range for typical desktop user tho

* https://www.youtube.com/watch?v=xQ3oJlt4GrI

It's called direct die cooling and that's pretty much what happens in the laptops. The reason why the IHS was introduced some 20 years back was the cracking of the silicon while mounting a cooler on top of it was quite easy.

neat. something like an integrated heat spreader? that's a pretty good idea