You can instrument the container itself (the environment in which RCE against PHP would provide an attacker).
You can't instrument the container engine or the host server, because AWS owns the security of those. But AWS will do a better job with those than you will, or at least, your whole usage of AWS is premised on that.
How often do people actually instrument their containers? I guess my original premise is wrong if you can simply set up the same monitoring inside your container
You can't do the same things; for instance, some container instrumentation schemes want an LKM to be resident, and that obviously won't work on Fargate. But you can generally accomplish the same goals.
You can't instrument the container engine or the host server, because AWS owns the security of those. But AWS will do a better job with those than you will, or at least, your whole usage of AWS is premised on that.