As Ben says, the 'new' shells are a bit lacking in quality of fit and at over £10k are expensive. When you consider that even after spending that sort of money you are just at the start of the restoration and a full interior and exterior re-paint will cost what, £2500 or more?
Thus the full rebuild, when you include all the other new parts you will need, plus a probable engine rebuild, you are looking at a 1991 Cooper which will have cost you around £20k if you include the original purchase price.
For that sort of money you could buy two restored cars of the same sort of age. I reckon my 1990 Cooper 1275 road-rally car, which is completely rust free, just re-painted with a newly rebuilt engine, new 008 tyres, 10" wheels and a Mk.1 front is worth maybe £10k.
Re-shelling with another used shell is widely done, although we cannot advocate doing it on here. The key here is "Don't tell him, Pike"!
If you can do the bodywork and your free/hobby time plus the cost of the panels and paint is the only financial outgoing, then it is worthwhile restoring your own shell. For example, I paid £3,000 for my 1990 rally Cooper and it was in poor condition. The total cost of panels (mainly pattern parts) was about £350, engine parts were £150, gearbox rebuild was £300, paint was £250, 10" wheel conversion was £250 and sundries were £300. The work was all done by me during the Covid lockdown and I am retired anyway. I am in profit if my time is ignored, but to pay for the work to be done will not be cheap. I know that if I couldn't do everything myself, classic car ownership would be unaffordable.
Good luck with your project.