Emulators have been a divisive topic for quite a while. The majority of games on consoles that have emulators available allow them, but some games do not, for various reasons.
One common reason for banning the use of emulators is that the emulation is not always accurate on certain consoles. N64 emulation has been quite bad for a long time, with certain games not running at all in some cases. Genesis also does not have great emulation in comparison to consoles like NES and SNES. Some games ban the use of specific emulators, for reasons such as inaccurate framerate in comparison to actual console, or not handling RNG in the same way as console.
It is also quite trivial to cheat on emulator in certain games. The inputs can be scripted to allow for perfect execution, and some emulators like FCEUX for NES even have tools built into the emulator to allow automated inputs on each frame. Memory addresses can also be edited to allow for ideal RNG, making parts of the game faster. This is a bigger issue for people verifying runs than spliced videos, because it is often extremely difficult or impossible to tell if someone has used these tools instead of playing the game themselves.
There are many arguments for allowing the use of emulators though. One of the arguments that is brought up a lot is that letting people use emulators makes a lot of games more accessible, as they do not need to buy the game, a console and a capture card setup to record their runs. For some games this is an absolute necessity, as the rarity of the game makes it too hard to get your hands on a copy. This is not always the case, however - the expansion kit for F-Zero X costs over $1000, for example, yet the use of emulators is still banned. This is going to become a huge problem as time goes on, as games and consoles will eventually stop functioning properly and become rarer/more expensive.
Sometimes the argument extends beyond reason. Recently there has been a discussion over the use of emulators in Metroid on NES. It seems that some runners were using save states on emulator to reset the game to the title screen at the beginning of each run. The issue with this is that the game loads in all of the random elements like enemy spawns, item drops and patterns at the title screen, so every playthrough of the game is exactly the same without any difference. It means that you can keep resetting the game until you get a playthrough with perfect RNG loaded in at the title screen, and then just play that save state each time.
Rather than ban emulators, you could just get people to use an overlay to show that the emulator was reset and did not load a save state at the beginning of the run. I was watching some Metroid runners discuss this a while ago, and something bizarre happened. They started to test manipulating the RNG in Metroid by changing the console that was being used to play it, and seeing if the amount of time waited until reset and the chips in the console made any difference on getting consistent enemy patterns in the game. It did. So if it is possible to manipulate the RNG in Metroid just by having an NES with the right chips in the console, should those consoles be banned too?
It is a very tricky subject to discuss, as all games are different. I do think that the vast majority of games should allow emulation though, it's just going to become a necessity over time anyway when it is not possible to play them on console.
I think splitting up the leaderboards like that is a very bad idea. The whole point of the leaderboard is to have as many runs as possible on there, all following the same rules as defined by the community. There are also a lot of games that only have a few runs up on the leaderboard, and splitting that up seems pointless.
If enough people start playing the game in a way that does not currently have it's own leaderboard, like glitchless or pacifist runs, the leaderboard can be added as a different category. That way you still have all of the runners following a set of rules on the leaderboard, its just in a different section. Speedrunning as a whole is coming out of an era where everything was pretty much the wild west in terms of what was allowed, wasn't allowed, how runs were captured etc. I think it is very important to have some standardisation, the only issue is people pushing too far in that direction to the point where it doesn't make sense anymore.
I actually would choose vanilla SMB. There was an incident a while ago with Bioshock Infinite that sort of relates, where the community decided to apply a patch to the game to remove an element of RNG that was essential to the run, but had a low chance of happening. I think stuff like that completely misses the point. If there is an issue with the run, you don't just take it out of the run, you find a way around it. Obviously that is not possible to do with SMB wait times, but I don't think it's something that kills it as a speedgame, having some time to relax and think about the next split can be a good thing, particularly if you're working out what patterns you will get in 8-3 or something like that.
It is not a common thing to have a mod on SRC doing things that the community as a whole doesn't want. If that happens, they can be removed and replaced with someone who knows what needs to be done to the leaderboard.