Nowadays, using il est un / elle est une is typical from non native French speakers.

This form is not a grammatical mistake. It sounds archaic but might still be used in formal or literary contexts with the meaning “there is a”. It is never required.

See this reply to a question very similar to yours and that explains why c’est un(e) took the lead: https://french.stackexchange.com/a/14729/1109

Are there any times when I should be saying “il est un” or “elle est une”?

Almost: Il est une heure 😉

No, it means the same. My theory for that is simple, as « C’est un/une » or « Il/elle est » is shorter to say, it gets adopted and used a lot more in verbal’s form.