Not sure if you know that this forum is for discussing suggestions with fellow users, not for actually suggesting things. Not necessarily intuitive, but it’s explain in the pinned “read this first” post. Suggestions are submitted the same way bug reports are (also not really intuitive, though it makes sense).
But as you’re not the first to come up with that idea, which I like as well, just upvote this instead of filing a new suggestion:
https://boardgamearena.com/bug?id=145913
In the second comment on the suggestion I linked, there’s also a workaround for searching for one publisher’s games that are on BGA (via BGG).