tl;dr: -delete is not required by POSIX, -exec is.
Facts
POSIX 1003.1 man page for find specifies -exec but not -delete.
This means -exec should work virtually everywhere. I would be surprised finding find that has -delete without -exec. The opposite is quite possible. Especially lightweight systems that use busybox tend to provide basic command line options only.
E.g. I have an OpenWRT on one of my routers and its find understands -exec, it doesn't understand -delete.
Not having -delete is not a big deal when you have -exec rm …. On the other hand -delete cannot replace -exec in general. It's a wise design to allow omitting -delete first.
Personal experience, observations and opinions
The above should be the primary reason why -exec rm {} \; is so widely recommended. The secondary may be a snowball effect. Users read articles and examples, get familiar with -exec and publish their own commands (e.g. here on Super User). Some of them may not even know -delete exists.
Few times I have seen (or given) remarks like 'You can use -delete instead'. And the responses were like 'Thanks, I didn't know that'. I don't remember any response 'I know, but this is not POSIX'.
Having said all this I tend to mention -delete whenever -exec rm {} \; appears. The reason is -delete doesn't spawn a new process, while -exec rm {} \; invokes a separate rm for each matched file. If you cannot use -delete then your next thought should be -exec rm {} + that can remove multiple files with a single rm (still it will invoke rm more than once if needed).
Why isn't -exec … + widely recommended then? It might be because of its limitations. I can imagine an inexperienced user thinking 'This works with rm, let me use it with mv!' Then -exec mv {} foo/ + doesn't work because {} needs to be at the end, just before +. The user gets frustrated and runs back to mama Windows.
Recommending -delete is usually safe here on Super User, I think. Most questions specify "big" OS-es, find commands there are rich with options. And even if there's a user whose find is limited I will probably get feedback. He or she says the solution doesn't work for them and I suggest -exec rm … instead, explain the issue etc.
A standalone article that recommends -delete won't get such feedback. In case of any trouble a user will simply go to the next link returned by Google.