Board Game Arena

it's what you do when you're playing board games in person. Finish a game, start up something new with the same crowd.

You can already do something close to this.

Create a group of people you want to play with, then create a table and add a filter to allow only the members of that group.
After the game, create a table for another game and add the filter again.

If I am understanding you correctly I wouldn’t consider that as being close to the same. It sounds like basically the op wants the rematch button but instead of playing the same game to choose a different game. What you are suggesting is to create a group and then use the filter to limit a game to that group? Instead of having to create a new group each time you are playing multiple games w/ a certain set of people you can just use the my friends filter if that is the case. But then if you have a lot of friends some may join.

A "play again" button allowing to change the game, is quite the same as the lobby link in the main menu IMO.
The only difference is you have to apply the filter again.

You can create a group with only few of your friends in, then only those players will be able to join the table.

This is the annoying part: you have to create a group with only the players you want to play with at the moment, and then a new one if you want to play the next day with different friends.

If you play often with the same people, it seems quite enough to me.