A lot of times the chain of custody and the history is what makes a boat valuable or interesting and government recognition of the new boat is the difference between the original and the replica in a lot of people's eyes because without that recognition there is one boat and with it there is two, a real one and a replica. Sometimes people just work done right and if the hassle of creating a "new" vessel in the eyes of the government can be reasonable avoided it will be (but this is rare reason, most of these people would rather buy a different boat, nobody does that kind of work on a boat that isn't historically interesting or of sentimental value).
It's common (as common as something can be in a niche part of a wealthy people's hobby) to have a boat in crap shape and park it in a shop, deconstruct it enough to take critical measurements and then rebuild it in the adjacent bay starting from the keel using all new material and then reinstall all the original fittings, hardware, etc, etc, off the original boat.
So yeah, you're "supposed" to re-title the boat with a new title in the same way that you're "supposed" to drive 55mph on a four lane interstate highway. In my observation the fraction of people who do what they're "supposed" to is about similar and those people tend to be motivated by special circumstances.
I assume commercial vessels follow the letter of the law but you don't exactly see a lot of commercial vessels getting keel repairs short of scrapping the vessel (or selling it overseas) and buying a new one.