In the state of Florida, if you're pulled over for any infraction then the driver gets the ticket (except click-it tickets, they can be given to passengers). However, if the infraction was only captured by a camera such as a red light camera or speed camera, then it gets issues based on plate, which would be the LLC. If the ticket isn't paid, then they would pursue legal action against the LLC which would fall on the registered owner, regardless if you were driving or not. If you weren't driving, then you'd take it to court and try to fight it which is usually easy enough to do because they can't prove that you were driving the vehicle.
Registration is a moot point if you get pulled over. Typically, the driver gets the ticket whether the car is registered in a different state, to a different owner, or not registered at all (just more tickets in this case). I'm curious to know if there is a state, county, or municipality where registration affects citations for moving violations.
To r3drckt's point about photo enforcement and the like (toll enforcement, air enforcement, etc.) the tags are used and unless you borrowed/stole the car, it will all come back to you as the registered owner of the LLC.
I planned on going the Montana route just for ease of registration (I'm in Illinois). The tax side of the equation wasn't even a consideration until I started researching it. It was one of the deciding factors for having my kit shipped versus picking it up after I researched everything. The cost savings to have it shipped plus LLC fees is significantly cheaper than the expense of picking up the kit and taxes, but I am also 900 miles away from Red Oak, TX, meaning the trip was not going to be cheap the week before xmas.