There are a significant number of good points from all perspectives of this discussion; however, I personally think video proof should be required for leaderboard submission.

I do not believe that leaderboard submission is necessary to start out as a runner, or to participate in the community as a runner. You may discuss times, strats, PBs, etc., but with regards to a comparative list for competitive purposes, especially with a large/growing community, an objective requirement for submission to such a list should be a standard.

For an example, in the scientific community, new scientific theories require proof through testing, and often are subject to peer review. The testing of such hypotheses is done to account for all variables. As far as I know, video proof accounts for just about all variables in a speedrun. This being said, runs are very different from theories - after all, speedrunning is a competitive hobby, not a scientific study. On the other hand, competitive hobbies such as sports and the like are done IRL, while speedrunning is almost entirely offline. Could a run be accepted if a certain number of members of the community or mods watched and confirmed the run IRL? I believe so, yes (except in the case of WR, like BB said).

With regards to expense and effort for capture/upload, you can capture video on your phone camera, a cheap video camera, or a webcam and upload the raw footage to YouTube. If you have a smartphone with a camera this is even easier as you can upload directly from the YouTube app, and just about everyone has mentioned EZCap. Someone would have to retime it (ideally, the runner), but regardless, it is possible.

Any hobby requires some level of effort and expenditure. Over the course of the last year I've spent over $3k just on music equipment, most of it entry level. In addition, I've spent over 9 years practicing music and taking my time before putting anything out. To draw more comparison to potato cam, I could technically record music on cheaper equipment - and I have, though not for profit. On top of this, music equipment is far more expensive than video capture equipment. It is because of this that I believe that any hobby you feel worth investing in is one that requires more effort and expenditure than just getting into it to get involved and not compare.