Most of the time it's not worth the risk to buy from a stranger. I think the only time I'd buy second hand is if I was going to use it literally once and I was really confident about the model etc and couldn't find a reasonable alternative new. There are quite a few lower cost models on the market so it's not usually necessary.
Or if the model I wanted was discontinued or extremely expensive new. For example I live abroad and the 25kg ERF seats cost about €400 here so I know a couple of people who bought them second hand, because they decided that second hand ERF was better than new FF.
I tend to think human nature is mostly good and most people won't put a child in danger knowingly. The problem is that other people might not realise that what they are doing is dangerous, they might think that the little repair they made is just cosmetic (when actually it affects a key structural part) or they might not see the accident they had as an accident (when you would) or they might think it's still fine even though it's several years old, or they might have missed the news about a safety recall.
You often do not get instructions with second hand seats, which can be a problem as using the car seat as designed/intended is extremely important. You can download instructions online but it might not always be easy to identify the model.
I've done an unofficial survey of seats for sale on marketplace too and found that just from what I could see from pictures, most of them particularly in the toddler stage had safety related issues. Either too old, missing inserts, some issue with the straps, some actually imported/illegal. About 5x as many dangerous as reasonable seats (and of course you can't always identify all issues from the picture). Included in the reasonable option was one with the incorrect insert in - this is another common issue, as people get them mixed up with the one from their pram, another seat, or just lose them and replace them with a separately bought one.
Some good budget options (new) for a second car for second stage:
Graco Extend R129
Graco Slimfit R129
Graco Turn2Me
All good safety, can be rear facing up to 4 years (ish), cost about £100-150 :)