Concerns about OGS’s “competing” product aside, i think OGS is already doing what it should w.r.t openness: exposing game data in SGF format.
A dedicated button for a specific review tool sounds well-intentioned, but the tight coupling can actually decrease openness.
Imagine a new offering pops up, ReviewHero.com. The offer a solid service, on the level of AI Sensei, perhaps even better. They ask OGS “Can we get added to your game screen as well?”. Now OGS is in a tough position, because they have to decide whether this new site meets the bar for further cluttering the interface. Or down the road, if one service becomes unmaintained - OGS then has to decide when to drop the button.
This is, of course, very hypothetical, but I think it’s a good reason many tools have “Export in some open format…” rather than “Open in some alternative product…”