it sounds like everything through the bridge would appear as coming from @web.brid.gy.

Because this is the only current deployment of the bridge. The code is open source, if you want to host/run/manage your own bridge, you can do it.

That was the same issue that I had with fediverser and alien.top. Everyone got so obsessed with the bots from alien.top and caused so much drama that no admin would be interested in using it for the “login with reddit” functionality. If there was a few more other instances running the software, it would have been incredibly more helpful to get people to move away from Reddit while helping bootstrap the niche communities here (which are until today completely lacking in content and not attractive at all for the masses).