The etiquette of conceding has been brought up before in various other forums, as it applies to games other than backgammon.
The basic outcome of the discussion was that some people like the final victory move and some people hate wasting time. About the only thing most people agree on is that if the game is impossible to win, don't play until the last move and then concede; that's incredibly unsporting. Generally the best action is for the loser to ask if the winner would mind if they concede. (Or the winner to
nicely suggest that time could be saved in a mathematically impossible situation.)
A couple of notes about the other issues raised:
Placing a "concede" button on this game is not a good idea. Game buttons are generated "within" the game, on the active player's turn. There already exists a concede mechanism for all games on this site, and that mechanism is outside the game. Attempting to alter that would at best cause confusion, and could easily introduce bugs.
A notification that the game is mathematically impossible would require much more programming. The development of games on BGA is done by volunteers, and it would be difficult to undertake that work unless a clear benefit could be achieved.
And, in the case of backgammon, even though it may be impossible to win perhaps the loser is playing to avoid a gammon/backgammon. True, multi-game sets are not implemented on this site, but there has been a lot of discussion about the doubling cube. Some people play this game in places other than this site
, and it may be standard policy for them to consider avoiding gammons.