It wasn't implemented because the CPU resources it would eat are better spent on other things, like making sure the game does not crawl due to calculating hundreds of NPC entities in the background, something no Crysis game ever had to do.
What does it have with entities during AI calculation? It was one of my specializations decade ago, AI and artificial life, you know stuff like wolves and various other stuff like forest growing and inventing algorithms that allows simulate whole ecosystem... Of course animation of each animal is real PITA and it's definitely infeasible in garage game era where one person on team is doing in spare time two other professions thus is saving money for hiring additional developers who would in effect cause drop of work efficiency (and before they would be able to do stuff, it would be deadline) If people were as willing to do stuff, and release stuff, for free as they were 20 years ago, there would be freely usable auto animal animation model easy to integrate into any project. Current development model where money earning is more important than in house research and development, and less important than technological and art advancement of industry doesn't create tools and skills for future. It's more like model where merchants found a way how to educate themselves in simple skills, and they are using these simple skills for profit. (And they are more interested in optimization of expenses than in actual industry improvement.)
AI goes async. One to 3 cores for simulations that goes into detail. Nearfield environment destruction is bound to graphic engine. It's typically solved by raytracing, and possibly by a buffer that holds calculated values until scene behind changes, assuming they don't pretend one bullet can slice off one tree, and keep calculation of damage per area until the possible damage moves over threshold for raytraced destructible geometry piece.
Then you have either trigger for pre-canned animation, or they handle things by bit more computationally intensive way. (While typical animation can look better, player might notice there is something bit weird, and sometimes alternative ways are used even when they look worse. Alternative ways do have a lot of advantages, but they are much more CPU intensive.) Still an elementary stuff like breakable trees might be doable for developers that didn't bought tools and used them as office lady, but rather wrote and developed major part of code in house. (Assuming they have at least 15 people in company.)
As for AI CPU intensiveness. I seen developers who had similarly fast stuff as I had, who compiled AI into DLL and simply restricted themselves by forcing RAM compatible model in rest of program. For me calculation of 100000+ AI was doable without problem. But of course I learned AI programming outside of school system, thus I didn't even have a chance to learn bad habits. And I think using scripting language for AI fucks stuff up.