Tyres will be considered illegal if they have insufficient tread, cracks or bulges. In addition if the inflation pressure is too low or too high. Notably there is nostipulation maximum tyre age for cars or trailers.
Tyres have a very important job to do, and the conditions in which they are expected to operate has a massive range, so it's inevitable that failures can arise at any age, but there is a wealth of historical data that does show some generalised trends.
The first and most obvious trend is that the more milage a tyre does the greater the wear will be as evidenced by the depth of tread. In general tread depth is not a problem for caravan owners. But it is most common on cars.
The second trend is that as tyres age, they are affected by tyre composition, environmental conditions, and will age wear. Some issues will be exacerbated by higher mileage, loading, poor inflation, misadjusted tracking and driving styles.
Some tyres are abused, such as driving under inflated, which flexes and wears the side walls more than expected. Kerbing, which reduces the wall thickness. Driving through big pot holes or driving up kerbs, which can damage the internals of the tyre without showing any outward evidence of damage
Unfortunately normal drivers cannot see inside the tyre walls (if they can the tyre is definitely in need of changing) so any normal inspection is limited to an external assessment.
Consequently whilst there might be no outward evidence of significant material degradation or other problems, increased age must be considered to present an increased risk of failure. Especially for such low milage trailers like caravans, tyre age should be significant factor in choosing when to change tyres.
Bearing in mind that caravans even when empty invariably weigh 85% of their MTPLM they are likely to be exploring most of their tyres load margins all the time. the age related wear even when standing is going to be more severe than for a the likes of a garden trailer which is empty most of the time.
The generalised advice for caravan tyre to be change between 5 and 7 years is an eminently sensible approach, and any one leaving them longer is really inviting problems.
One of the advantages of living in the UK are the tyre retailing laws, where tyres have to meet some important standards at least gives you some certainty that even budget tyres should be good enough for most trailer applications. I certainly would not recommend going for premium priced products as it would be a waste of money.