So far as the issue you raised is concerned, I've shown you what the rock bottom (WBAC) value of a 100,000 miles 2020 M3P is. Expect a M3LR to be less.
The cheapest 2020 LR on
Autotrader is a private sale 102k mile asking £33,490. I think that's fantasy land. The next cheapest is a 43k miler asking £36,500 which, given the seller is openly showing us their number plate, WBAC would give £31,180. In your position I'd be tempted to offer that seller (a doctor, no less, as if that makes a difference) a quick grand over the WBAC price and see what happens. But if you dont mind buying a 100,000 mile car, fine: having said that, I don't understand how your insurance would pay for a risk arising from mechanical failure (unless you careened into something solid when a wheel fell off, for example). For mechanical piece of mind you need a warranty.
I also dont see how anyone thinks that at a time of rampant price inflation any manufacturer, particularly one still in demand, is going to drop its prices.