Why is there a limited amount of time to buy AppleCare ?

Fundamentally, AppleCare+ is an insurance product.

AppleCare+ is intended to provide cover for a limited set of circumstances where a failure or accidental damage may occur. As with all insurance policies, you purchase cover (in advance) in the hope that you’ll never need it, but have the security of knowing that you’ll be able to avoid a large bill if something goes wrong or an accident were to occur.

Some people choose to not buy this (or any) insurance. In accepting a lower initial cost outlay, similarly accept that higher costs will be incurred if something were to happen later.

Insurance is pre-emptive. Insurance must be purchased before a disaster occurs or a fault becomes apparent - not after. Apple are generous in allowing you 60-days to take the option to purchase cover - after which the option is lost. An open-ended period invites attempts to commit insurance fraud.

Because most extended warranties for electronics require you to but it at the time of purchase or within a certain time period. Otherwise people will try to wait until something is wrong and then get it. The amount of time is quite generous. 60 days.

I’m amazed it’s as long as 60 days. Question for you - why would any company be willing to suddenly give an extended warranty on a device that’s been used in the wild for months or even years?