Claude does the same when you hit the context limit, but the difference is that claude's context limit is 1m and Codex's is 272k now. Claude lets you get a lot more done before you have to worry about the start getting compacted away.
Not really, on the project I'm working on right now most of my longer prompts seems to consume somewhere between 300k and 400k tokens (input + output) and I find that both Opus 4.8 and Fable 5 don't seem to get lost with that much context. At least the results still look good to me.
I don't think I've ever pushed past 500k though, it may well fall apart at the higher end of what is officially supported.