DL from different state than car registration? a problem?

I have a small business that has me traveling about 6 months out of each year, away from home, all over the USA. When Im not working I live in KC. I maintain a house in KC. Doubtful Ill be moving anytime soon.

But I got my car registrations renewal the other day and annoyed with how expensive it is to own cars in Kansas.....And I have been thinking of creating an LLC to protect personal assets.

Thing is - I think I can create the LLC in any state I want (through a registered agent and mail forwarding service) and doing it in MT or SD, as opposed to where I live in KS, could save me about $1500 on car taxes each year. So putting my vehicles under ownership of the LLC I might create will hit two birds here - lower the cost of license plates each year and protect my assets.

I know this isnt outright illegal, but what happens when I get stopped and I hand police a registration from SD or MT, but my license is KS? Is that a problem?

Opinions and advice wanted....even if its contrary. Let me have it folks.