No, "coins are good" doesn't mean "you must collect all coins." Coins are good in Mario too, but they're not mandatory.

But one of them doesn't say it's required. I can finish a level in Sonic without collecting all the rings, even though rings are a good thing.

it's to avoid people having to go back in the level to get coins they thought were 'good' but optional.

I bet it's not as strong as the annoyance of missing them and then realizing at the end that you need them.