My hangar neighbor has a 182RG with 2600 hours on the original engine, and it's not had a cylinder replaced. Local club has an Archer with 2700 hours since the last major, I do think it's had a top done once or twice though. They're out there. I wonder how many perfectly good engines are overhauled simply because they're at the recommended TBO time.
The way I look at it, if oil analysis is good, and compressions are good, engine runs well, no reason to mess with it. That doesn't mean I wouldn't still consider doing a major once it got well past TBO, say 500 hours past, but I definitely wouldn't automatically decide it's time for a major just because we are at TBO.
As far as picking an airplane... If I could do it again I'd either buy an airplane with a recently(under 200 hours) overhauled engine, or buy one that's close to run out, priced accordingly, and expect to do a major after perhaps a couple hundred hours of flight time. Finding one that's been flown often, 100 or so hours a year, regardless of total time, is also a good idea. Much less chance of corrosion due to sitting idle.
Mid-time, you're gambling. The airplane is priced accordingly, and there's no guarantee of how much farther it will go. You could end up like me, buy it, fly it 97 hours, and oops, time for a full overhaul.