Phone lag also slows down the time

As JDMI said, lag can cause inconsistencies in the end time of each level. This would make it so that runs are based on luck alone, and being forced to nerf your hardware if you wanna contend. On the other hand, RTA's downside is requiring faster menuing, which I assume most people can agree that it isn't a big deal.

I mean that's fair to say but I do think that emulator should be separated on full game runs because I would think it is way easier to menu for them

Technically they are separated, so long as people label their runs honestly.

But the world record of Dence Forest says android emu so do you mean it's in the wrong place or do you mean that if people look close they can tell what are phone and what are emulator??? Just curious what you mean

There's an emulator checkbox you can tick if the run was done in an emulator. Then, if you go to filter, you can hide emulators and just show original hardware runs.

Considering how most people play the game on their phones I doubt that making emulators into their own category would make it better.

No need to separate emus and phones since among phones themselves there are tremendous hardware and subsequently performance differences.

Also its not a big deal to do the menuing between each stage as it's always literally just press one specific area of the screen.