It's how long is a piece of string question... I took on a 17yo ex eventer on full loan, for free, who then broke down with what I now know was a pre-existing injury and the owners basically said it's on you and washed their hands of him. Essentially getting themselves out of the responsibility for making the call I believe. So this could be the case at any price point.
I also know of many people who have taken on older horses and learnt lots from them and have had them a few years and retired them, filling their intended purpose perfectly. On the other hand I have also had to PTS a 7yo, who I bought as being diagnosed wobblers as a 2yo, and who had been a low level all rounder for Navicular; and an 11yo who had been high mileage and was covered in sarcoids, for being completely broken down mechanically. So even if you think you know what will be the end of them eventually and take a calculated risk, it could be something else.. I could actually have probably sold him on when I saw some issues creeping in for a lot of money, and his big paces and athleticism would have made it hard to pick up on anything as he so easily compensated in other ways.
Age, price, history, conformation etc are all pretty meaningless essentially. You have to either take a punt or decide against it. It's more likley a 19yo won't have longevity, or could have an injury but you could equally buy a 6yo with the same..
Not helpful I know, but you could chase the answer to an unanswerable question all day - only you know the risk you're willing to take. It sounds to me like your gut is saying no, and you should always listen to it.