Can you provide example(s) of the broken query with non-GROUP BY columns in an aggregation? (Or a reference link if this is well known - I've searched briefly but can't find anything.)
TBH I like the ability to do this. Sometimes you truly don't care which value you get, you just want one. Sometimes you have application-level constraints which mean the one it picks is guaranteed to be correct, but you can avoid the cost of enforcing that (at insertion time and at lookup time). It's a handy tool when it's appropriate.
But hell yes, tools should warn you about this loudly, as it's not generally correct.
Can you provide example(s) of the broken query with non-GROUP BY columns in an aggregation? (Or a reference link if this is well known - I've searched briefly but can't find anything.)