I think this would be a good addition, if it's not to much trouble to program. What is the shortest/longest speedrun? or What is a game between x and y minutes? are really frequent questions.

I've been wanting to add this, but haven't so far because of some issues (probably solvable but I haven't had the time). If the length of a game is simply taken as the shortest run for it, it would just become a huge list of tiny ILs. If it only uses fullgame runs, that makes it unusable for all IL-focused games which is less than ideal, and it would still be just a list of games which happen to have short fullgame categories. Using the first/default category would mostly solve that, but it's not like the default category is the only one worth running for all games. Not just that, it would also have to use the default subcategory, and the defaults for any settings (variables, emulator shown by default etc).

What you end up with is a sort which does not really work for a lot of games. Complicating things further, the leaderboard may exclude load times or use IGT which isn't a problem for sorting, but say you're looking for a 1h long game to run finding games which are 1h IGT but 1:30 in real time isn't all that useful. Similarly but to a lesser extent, games for which the WR is very optimized would also show up higher than you'd want them to.

Given the number of moving parts in all this, determining the fastest time like this would be pretty computationally expensive - not something that can be casually done for thousands of games in real time. Of course it's possible to calculate it separately and cache it, but at that point it seems like a lot of implementation work for something that fails to be useful in a lot of cases. It would also add more overhead in development as any time leaderboard options are added/changed, the sorting would most likely break without being adapted.

But maybe I'm thinking way too complicated, and there are actually simple alternatives to alleviate these problems you can come up with. I'd be happy to look into it again if that's the case.

Also whether the sort is added or not, I would say "What is the shortest/longest speedrun?" is better suited to be answered by a general stats page.