I have personally been targeted by one of the states I live in for Montana Plates. For me, it was a pretty easy ordeal and all handled roadside without the need to visit the local tax office or deal with the state.
The primary reason the state troopers are pulling over the MT plates is they are expecting to find an LLC, and then they will interrogate them.
I was driving a truck with the local state plates on it, pulling a 45Ft flatbed trailer with MT plates. I had the paperwork for the trailer showing it registered in my name, that matched my driver's license (not MT). That ended the inquiry.
Getting plates with an LLC name behind it will become an issue for drivers in states that charge a vehicle sales tax or registration fee annually.
The first requirement of getting a MT registration is to establish a domicile. This means that you either own or rent property in the state and pay utilities, property taxes, and have a bank & credit card for the address. Having those properties in an LLC is another legal way to own a vehicle in the same LLC but will be subject to more scrutiny.
When the plates are run and the name matches the driver's license, the inquiry ends immediately, and no further actions are taken roadside.