It's certainly also true for astronomy, quantum gravity, and most of the condensed matter physicists that I know. Which subfields don't involve at least Monte Carlo simulations or writing code to analyze data and/or control experimental apparatus?
Analytical work dominates in high-energy theory, quantum information, mathematical physics, cosmology theory. I'll also dispute your characterization of quantum gravity with my own anecdotal experience. If we wanted to solve this, I think we'd just open up an issue of Physical Review and count whether more than half the papers are numerical.
Outside big collaborations (e.g., particles, astronomy), my impression is that most experimental work is not writing code even though rudimentary code is of course needed for data analysis and equipment control.
We're on a site for programers, so I think the former physicists who happen to be here are unrepresentative.
Yes, but most physicists are not theorists.