AES is one of the few that I'm pretty confident will be around for a while. RSA already has a lot of caveats to its use and they will undoubtedly grow. In my completely uneducated opinion, it's even odds on RSA vs ECC first.

As long as you’re using it correctly RSA should work, right? We’re not going to factor big numbers anytime soon and RSA is pretty much about factoring.

RSA key sizes have gone up constantly over the years exactly because we did factor ever bigger numbers. ECC key sizes are the same as when the schemes were new, that's one reason ECC is better.

Yes, but in the real world there are a lot of opportunities for implementation failure.

I completely agree.

My real unpopular opinion: designing a secure asymmetric cipher is much harder than symmetric.