I agree 100 % TTR. But the catch 22 for me is the addition I have to make to your list of exceptions " something extremely unique, rare and valuable " That would be the addition of affordable on a pretty slim , retired guy budget.
In my case I like cars that almost fall into your category except the examples I can afford are run down, derelict, crashed , burned, partially parted out specimens of very off the mainstream sports cars. Early Lotus, TVR , Morgan , Elva and a host of others. And so many times if I find one the paperwork vanished decades ago. I grew up with these cars and owned a number of them in my youth. Then the early 1980's recession hit my area particularly hard and the vast majority of them ended up Stateside or back in the U.K. or Western Europe.
With the current cost of living situation in Western Canada these days each year a few more of what's left of the local car inventory also leave. As people age out of ownership the local pool of people with the interest and means to take over ownership shrinks faster than the rate at which cars become available and Bring a Trailer etc. makes another out of the area sale.
If I could afford to just buy a decent one with no problems I would. But we all face our own challenges in life and mine is the impossibility of just going out and paying the going rate for a no problem example. A couple of cars and several vintage British motorcycles I have been piecing together for decades . 1963 TVR Grantura MK3, 1959 Buckler MK 15. 1949 Triumph Trophy 500, 1954 BSA Gold Star 500, 1953 BSA Super Flash. If I am lucky I might even get to drive / ride one in my lifetime.
Most of the fragments / hulks I find are in the U.S. , I look endlessly on all the club and one make forums. That is where the whole title hurdle comes into play. Years ago it was not a problem. These days it is almost always a deal breaker. Nearly all of these cars will eventually have their paperwork problems solved. Huge amount of interest and relatively few cars to go around. But I don't have any U.S. property to store them on while I wind through the various ways to re establish a title. I have often thought of buying a small place next door in Washington State for that purpose, but property has really shot up there over the last 20 years. Nearest place where things are still dirt cheap is South Eastern Oregon, but that is quite a long way away. How many hoops do you jump through before you just throw in the towel ?