I did a Jumpless run for fun and I think it would make a good addition to the leaderboards. Having 2 categories seems fun and i don't think this would do any harm to the current leaderboards.

Here is a run i did of it:

2 years late but this seems unecessary, if you can't jump you're going to remain the same walking speed 99% of the time so most runs would be roughly the same time anyway.