I don't think that tells you anything without comparing to the infinitude of composites too. The fraction of numbers less than n that are prime is roughly 1/logn, which goes to zero in the limit. So I think the limit of numbers with factors less than n as n goes to infinity must indeed be 100%.

That doesn't mean there's an n with 100%, just that there's no smaller limit that some n doesn't exceed.

The primes become more sparse in the integers as you go farther. For most reasonable definitions of the density of composite integers in the integers, the density would be 100%.

Iirc, it is believed that the number of primes less than n is O(n/log(n)), so primes/integers among the first n integers should go as O(1/log(n)), so goes to 0 as n goes to infinity.

There are infinite perfect squares also, but only 0% of all integers are perfect squares.