I think chess.com will also soon adopt that. It is very necessary now a days!
Yes! We should have different categories in bullet chess.

Totally agree, lichess already has a separate ultrabullet category so it wouldn't be radical for chess.com to implement this.

My understanding is there are plans to add a hyper-bullet category, though I haven't heard how far along that plan is.
Yes! We should have different categories in bullet chess:
1. Bullet (1 minute)
2. Bullet (30 seconds)
3. Bullet (30 seconds below)
All these categories should have its own points and ratings. One category's points and ratings should not affect the points and ratings of the other. And also, there must be separate icons in chess.com to select these. I hope chess.com will look into this in future.
Now a days, there are so many people addicted to bullet chess, especially for fun.
A study says that bullet chess helps us think faster and make a conclusion about different situations in life quicker.