Yeah, because millions of hours of service use over decades constitutes an arbitrary number...
Whether an engine requires replacement before, during, or at TBO has a tremendous amount to do with how you treat it and frequency of use. It's a good reference guideline that will help you estimate how long you can go prior to. If you're operating Part 91, though, it doesn't mean you necessarily need to replace your engine when it hits that magic number.
There's always the question of whether or not it makes sense to overhaul it, though. For example, I have one friend at Williamsport who has 1900 hours on his factory overhauled engines in his Aztec. The engines themselves don't leak oil, have good compression, good oil pressure, etc. The fuel injection servos are wearing out, along with a number of other little things on them. To some people, especially if dispatchability is important, it makes sense to just overhaul the thing and get all the new parts. It's a more complicated question, and one you have to figure out the proper answer for yourself.