Are you suggesting developers would start adding bugs for the purpose of killing them off later?
FYI, we've had this system at Twisted for a long time, and that hasn't really happened. When it was first introduced, I argued that it might lead people to review too much; then Glyph counterargued that that's a feature, not a bug. History's proven him right.
It could be that because it's an open source project, and most development on it is by volunteers, that that mechanic is less strong: it's not like people collect bonuses or anything because of their scores... Nor would I suggest that in any other context :)
If you start measuring some metric, the team will adapt at improving that metric, but inevitably this will spill out into distorting or lowering performance in some other aspect. So as you point out, such survivor board might make team focus on fixing trivial/easy issues, but the issues requiring big time investment might go unfixed (as it would make 10 trivial issues pile up while you fix 1 old hard ticket - which will make you look bad).
This is anecdotal evidence, but this hasn't happened in over 2 years of having this thing at Twisted. People understand it's fun and games, and it is not the true measure of success. Real success, including bringing in old/hard tickets, doing release management... etc is very much celebrated, even if it's not visible on the board.
Another comment that has been made here is that you shouldn't have giant monstro-tickets: they should be split up wherever possible. Clearly that's not possible in every case, but the point is that monstro-tickets aught to be the rare case.