Don't know if it's still the case, but a lot of used tyres were imported from Germany where the laws on tyres fitted to a car are much stricter than here. It is not permitted to have different brands on an axle for example, and winter tyres are compulsory. I've certainly seen plenty of UK cars fitted with 3 "regular" and one winter tyre which almost certainly came from a "part worn" supplier.
As said by others, carcasses and rubber compounds harden with time, a 10yr old tyre may look perfectly OK but it won't perform like a new one regardless of the make or how it's been used or stored.
I recently changed the tyres on one of my bikes. It does few miles and while they were less than 1/2 worn they were about 7yrs old. Compared to the new ones the old tyres were like wood, pushing a thumbnail into the tread showed the old and new to be like chalk and cheese (or rubber and wood even).
If cost was crucial I would choose the cheapest new tyre rather than any used "part worn" item, but each to their own choice. I understand not everyone has the luxury of a few ££ spare cash.
Personally I tend to look at the marginal cost of things. I've made the mistake in the past of not paying an extra 10% for the premium brand, and regretting it. The more something costs the more inclined I am to paying extra for the premium version, I usually soon forget the extra cost but I'm reminded of the lower quality every time I use an item (a reworded version of a classic statement). Of course everyone has to work within their budget.
Remember, the tyres are what take you directly to the scene of the accident.