I believe I would've at least registered a primary caliber and then list some alternates compared to just saying "MULTI". But if the examiner doesn't like it, I'm sure they'll send the forms back to you and delay it a while so you can make up your mind which one(s) you want to list and use. They'll give you 30 days to decide.
My AR SBR is registered in Primary: 5.56x45/.223 Rem.
Alternates are: 7.62x39, and 6.8 SPC.
I would've registered it in 9x19mm also, but I have an MP5-K SBR registered in that caliber, so I wasn't really needing or wanting another in that chambering.
For a fun gun (range) nothing wrong with 9mm at all. Ammo is cheap and that just equals to more trigger time for less money.
Plus if you use an indoor range, they're generally allowed there too whereas many higher power calibers aren't.
The reason a lot of SWAT is moving away from the 9mm is the lack of armor penetration. That isn't a concern of mine, so I don't see anything wrong with the 9mm. For the most part, it is very rare for LEO's to encounter a tango sporting Kevlar anyway. That's why my opinion goes against the norm nowadays.
Is it a bad idea for an LEO round? Or a Military round? Not entirely, but when a team is moving in on a hostile, it's nice to know that you don't have to second guess and hence, why a lot of SRT's are moving away from the 9. Peace of mind is all. Are there better rounds available for certain applications? Of course, but just keep in mind, there is no one perfect round for everything and you can't carry everything at the same time.
My 2 cents.