They do below a certain point yes. But at that point you just buy another one and drive it until the engine falls out. This is how most people operate.
On my vehicle an engine costs about £1275 to put a refurb in it. Gearbox about £550.
There is no rust anywhere on my 8 year old vehicle.
People run like this out of financial necessity. They don’t have enough income to run an EV.
So batteries on EVs generally don't fail dramatically, they slowly lose range over time.
So someone buying a used EV will presumably buy something with enough range for them to get around, and then over time if they notice the range starting to decline to the point that it might be an issue, they'll have some time to save up & trade in their car for a better one. Their current car won't be worthless on the used market and someone who doesn't have as large of range requirements (e.g. a 2nd car for commuting) will still buy it.
There are other issues that can prevent an EV from charging at all, but they have usually cheaper fixes than a whole battery pack replacement like you're talking about.
May be UK is especially cheap for car repair but costs you mention are unrealistic for major repairs on those components. I had gearbox problems on 10 year old car and independent mechanic suggested to sell car to scrap yard - in his opinion trying to fix it will end up costing more than car is worth. It was before Covid inflated used car prices though.
From quick check in google: If you are extremely lucky, you’ll get your transmission replacement completed for $2,500 all in. If yours is one of the more expensive types, it could easily range to $6,000 or even more.
On my vehicle an engine costs about £1275 to put a refurb in it. Gearbox about £550.
There is no rust anywhere on my 8 year old vehicle.
People run like this out of financial necessity. They don’t have enough income to run an EV.