Could we have bullet tournaments?

I would love to see bullet tournaments in Chess.com Online USCF Tournaments once in a while.

There's no USCF bullet rating.

I believe 3 2 is the fastest USCF rated event that is currently allowed.

Bullet is terrible for actually improving at chess. I've stopped playing it altogether.

5|0 is technically faster but 3|2 has a lesser base time 

Correct, bullet is not an allowed US Chess format and can't be rated.

The fastest that can be rated is base+increment/delay = 5, with a minimum base of 3. So, as mentioned, 3|2 is the lowest.

I don't think it's a good idea to hold events in the club that are not US Chess rated; we had one exception in the past and that was a match with the ECF.