The question of what players who feel that they don’t have a chance anymore should do is interesting and a bit problematic. I believe this is the reason for including the “elimination” mechanic, but as we’re seeing it’s not easy to eliminate a player completely. I think we should provide some clearer incentives for losing players in the rules for the next game (for instance, is it really better to have only winners and losers, compared to competing for 4th and 5th place?). But this is a tricky problem in general and there probably is no perfect solution.
Edit: One possible idea is to have each players score be how many points they are behind the first place player(s). So let’s say one player has 30 points, one player has 27 points, one player has 24 points, and the remaining two have no alive stones. You could say that the first player has 0 points, second player has -3 points, third player has -6 points, and remaining two have -30. If your incentive is to maximize your own score here, it is in your interest to keep attacking the leading player, even if you can’t keep any of your own stones alive. You could use this rule together with or instead of the current elimination mechanic.