PERF: Defer setting of distributed cache in more spots. (PR #13263)

See follow up commit for rational.

Follow-up to 8cfe203383367cc7a3cf31b3c3960b7b7aac92ef

GitHub

The title of this pull request changed from “PERF: Defer setting of cache in Theme.lookup_field.” to "PERF: Defer setting of distributed cache in more spots.

Thank you for reviewing @eviltrout