While they're not really active anymore, some runners have done runs of multiple NGs back to back, such as InfestedRiche and Arcus who have both done the Ninja Gaiden NES Trilogy back to back(Riche holds the unofficial world record according to Arcus).

Multigame leaderboards do exist, but I assume it's up to the moderators of a series to request them.

Here's one example: https://www.speedrun.com/multiff

(you can find more if you look for "multi" in speedrun.com's searchbar)

I don't see a problem with it. If no one has any complaints I'll add it