Interestingly I can think of a couple games that get around the mon-game issue you mentioned, and in pretty different ways.
Ooblets (which I haven't played, but appears to be popular with 91% positive on Steam) has you grow your mons in a garden, and rather than pitting them in fights with other critters, you do dance battles. It appears to be a bit more slice-of-life vibes but with the monster-collecting element.
And Cassette Beasts (which I have played, would recommend to anyone who likes monster collectors easily, and is 96% positive on Steam) dodges the issue in a different way. You don't actually capture and train monsters... you record them, and that recording lets you transform into that kind of critter. Successfully record a Traffikrab in a fight, and you can then transform into one later. You are still fighting the wild ones, but you aren't enslaving any or having them fight for or serve you in any way. The equivalent of trainer battles is fighting other people who also do this.
I think there's a couple reasons they do it this way.
One is that the pre-order bonus is still available despite the game effectively being out. I imagine they spare themselves some unwanted difficulty or dissatisfied responses from people who otherwise would have missed it.
The other is this very thread. Server issues are common on an expansion pack release. This gives them a convenient excuse to put in the apology announcement. It's a small thing but who knows, maybe it has some impact.
It's definitely a silly twisting of words (and their double key system for the pre-order and full purchase only sillier).