I echo what dklawson has to say. I have a 1971 Mini Cooper replica. And I am not hung up because it isn't a real Cooper S.
It looks like a Mini Cooper S with 10" wheels on Yokohama rubber, 7.5" disc brakes, red coachwork, with a white roof, but is equipped with a later A+ engine from a Metro, and bored out to 1380cc.
It's got a roll cage, bucket seats, and race harnesses because it was built for rallying.
Thing is, I would never refer to it as a Cooper, because it doesn't have that car's provenance, but does it really matter? It does everything the Mini-Cooper S did - in fact its performance is probably a sight better than the fabled S - and was built to inherit much of the S' features with the exception of Hydrolastic suspension, the close-ratio tranmission, interior trim, and twin carburettors.
The point is that you might think that the Cooper S is the ultimate Mini, but you will pay a premium for the name, as we do here in the UK. Whereas you could get yourself a car that looks like a Cooper, goes like a Cooper, and smells like a Cooper, by mixing and matching readily-available bits, and even if it doesn't say Cooper S on the boot (trunk?)lid it will give much the same kind of driving experience. And it won't be as expensive.
That's because even though the Cooper S was a specialised piece of kit back in the mid-to-early Sixties, much of that experience was fed back into later BMC/BL front drivers, most notably the adoption of the bigger 1275cc engine.
Admittedly, the 'mass-produced' 1275cc engine was not as nicely assembled from very high quality components as the relatively-low volume S unit, but it was still reliable - by Mini standards - still susceptible to the same kind of tuning methods as the S, and much more plentiful.
Hydrolastic suspension was an interesting concept and had huge development potential, but most Mini enthusiasts prefer the simplicity of the 'rubber cone' suspension, even if it is comparatively stiff-riding. Havng said that, a stiff ride is something you will have to put up with in any Mini.
Actually, there is a half-way house between the relatively pliant ride of a Hydrolastic Mini, and the harshness of the standard rubber cones: Dr Moulton's Smootharide rubber springs. Dr Moulton originated both types of Mini suspension, but after Hydrolastic was axed by British Leyland on cost grounds, he decided to turn his attention back to the rubber springs that he only ever developed as a stop-gap measure. In the mid-Seventies he designed a better riding 'rubber' suspension but this was never adopted on production cars. Smootharide was, however, made available as a kit and it is still available. Check out
https://www.minisport.com
I have these springs on my car, and although it will never match a Lincoln for ride comfort, you can actually feel the suspension absorbing bumps now and again. And that's not something you can say of the standard 'cones.'
So, by all means covet a Cooper S, but don't think it's the be all and end all. Any Mini can be adapted to do everything
the S did, but a good replica will cost you less.