Depends on the state. In Massachusetts, the rebuilder has to bring the car in front of the State Police with receipts for every single thing that is on the insurance list for replacement. If a flood car, all the electronics have to be replaced and connectors re-pinned or replaced. This is an extensive amount of work and very expensive to do.
In some of the poorer southern states, you basically bring a napkin to the DMV that says "I fixt it" and they say it's all good to go.
In general, a rebuilt title car is worth 50-60% of the clean title value. Some insurance companies won't insure them and if it's a relatively new car, it no longer will be covered by the manufacturer's warranty.
There are rebuilt title cars that can be worth considering. Lotus Elise and Exige will be totaled from something as small as hitting a raccoon. The "clam" is pretty much the entire front end. Lotus says they can't be repaired because they're an integral part of the crash structure, so only replacement is allowed. Back orders from England are longer than most insurance companies allow for repair, so the car gets totaled and sold at auction. You MUST know the history and have before pictures of these cars because the chassis is bonded aluminum and cannot be repaired. If there's a bend movement of a suspension pick up point, the car is scrap.