Wrong economic analysis. Try comparing the £2,000 replacement cost with the cost of a replacement vehicle which will have comparable service life. That £1,500 one you get isn't likely to last.
The only time your analysis makes sense is if you are still insuring the car against loss, and total it in an accident shortly after the repair. Since it rarely makes sense to insure an older car like that against loss it just doesn't apply.
Let's assume that the car still drives, but the automatic box, is beginning to play up. Hence the £2,000 quote for a professional/decent repair.
You can take the £2,000
and add to that the sale or part exchange value of your existing (faulty) vehicle, which might be £750, i.e. about half of the £1,500 if it was fully working.
So you have £2,750 if you sell (or part exchange it) it now and keep the money you could have spent on having the car repaired.
So if you can put another £1000 towards your next one.
You can start looking at cars for £3,750 and maybe more. Which can then be considerably newer, lower mileage on the clock and maybe better. This should be economically better (in the longer term). Than struggling on with your old, high mileage, only worth at best £1,500 existing car.
tl;dr
You are better off with a £3,000 or more replacement car (£2000 repair and £750 for the old faulty one), than struggling with a £1,500 old one, with a replacement automatic gearbox, which even from a decent/professional supplier, may still give some trouble, especially in the longer term.
But anyway, I fully accept that opinions about cars, and which ones to get. Also when/if to repair rather than replace, can vary a lot. So I'm happy if we disagree.
If there was a perfect/agreed solution. We would all probably be driving around in it. Which might get rather tedious and boring.
You can have any colour you like as long as it is Black.
You can have any type or shape, as long as it is identical to the Ford Model T (in Black).