The Mini One or Cooper can respond well to a performance camshaft swap actually, there are several options available for this depending on what you might want to do or achieve, if you fancy going down this path. A mild camshaft might do ok with something like the Bluefin which on your car will also give you full throttle which is the only difference between a One and the Cooper, bar the exhaust cat back I think, and it will run smoothly with no driveability issues. A Bluefin isn't really recommended by those tuning for even more power, with it's generic maps it isn't really regarded by some as engine safe, no generic map is on the R53 really.
I believe some that say not to tune a N/A Mini like these fitted with the Tritec engine, possibly haven't done it. Mine went quite well and back then only had an Autologic generic map with a fast road cam I was testing and a K&N filter element, not recommended on skinny 'T' rated tyres haha, but it was unassuming and also quite fun, that was a 2005 facelift One. If I'd added stuff I that I have now on my 53 for that car it would have been great fun, it drove straight to 130+ then without a custom tune that it should've had really, not exactly slow, great on motorways as for what it was it just cleared off.
When you consider R53 engine parts fit the One engine too there is more that can be done to build on the performance that a camshaft alone might give, JCW head maybe, forged parts etc.
A tuned naturally aspirated car can be a real hoot.