Here is the same constellation on finite boards of three sizes, white to move.
The ideal continuation (which I will not mention here) is the same on each of the boards. And also the same on an infinite board.
In this example it is clear that, at some point, the existence of more squares further away makes no difference, when we assume reasonably strong play.
But that will also be true for entire games. On an infinite board we could move our Queen 29356985738573427565984759875 squares away, but there is no point in doing so.
Each game could be re-played afterwards on a large but finite board with each move doing exactly the same.
This is why I will say that infinite chess is essentially finite chess.
On infinitechess.org I practiced QBB versus K, and I played one game. The game went quick an a lot of trivial mistakes happened.
But it was fun. I think that this website is really great.
Discussions about this website focus mainly on live play and features of the website. That does not yet answer one of my questions.
What is it like to play this game with stronger play and more thinking time? Will the games become too long, will we see too many draws?