Databases really do make you pay dearly for mistakes, and new linguistic functionality is not implemented with performance in mind.
I’ve written before about how to approach date math in where clauses: Where To Do Date Math In Your Where Clause
And it turns out that this lesson is brutally true if you need to pass time zones around, too.
Read the whole thing. In this respect,
AT TIME ZONE is similar to pretty much all other date operators and functions.