£1500 is probably a fair cost for the chassis welding and the other essentials. You could try for better estimates.
If a 16 year old car is otherwise in excellent condition and likely to last at least 2 more years without further expense it might be worth spending £1500 getting it MOT'd. But the garage have possibly taken into account the advisories ,lurking rust etc are only going to get worse and you might only get one more year before it fails the MOT again.
And thats assuming its 16 year old CVT gearbox doesnt need expensive repairs before then . Some cars are scrapped just because their CVT gearboxes are beyond economic repair. Indeed if your gearbox is in full working order it might fetch a bit above the odds as a donor car even without an MOT.
. If you spent £1500 on repairs then sold the car immediately, with a new MOT you might get slightly more than it cost to repair, but not much more.
It can be a hard decision, but plenty of cars go into the crusher with not that much wrong with them.