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I did what you're describing and it worked out well for me, but YMMV. Here's what I did:
I got an undergrad degree in physics, and was hired right out of school by a government contractor. My only hard skill from the degree was coding in LabVIEW, something I never have done in the workplace. Arguably my only real use in my first job was to be a person who submitted a timesheet that could be billed as a person with a STEM degree.
I changed jobs for a much better contractor where I did a lot of "system engineering" style analysis with MatLab, which I mostly learned on the job, and eventually moved into Python which I learned entirely on the job. Python really resonated with me, particularly using it for Data Science applications. I got a Masters degree in Applied Physics from a highly renowned school taking after hours courses that my job paid for. Most of the courses had no conceivable application to my day job.
I eventually was hired away from the contracting world and am a Data Engineer for a private company.
The thing a physics degree truly demonstrates is the ability to learn difficult concepts, think analytically, and have the math to back it up. If you go this route, you'll kind of be a generalist right out of the gate and need to be open to trying a bunch of new things to figure out what works for you. A master's degree certainly helps, and learning a useful programming language really helps. Be prepared to start somewhere as an analyst, and build from there.
Thanks for your perspective, it's super helpful.
Was your physics degree a second degree or your first/primary?
It's interesting to hear Python was so useful as I've wondered whether hiring managers snub their nose at Python (it's the only language I have semi-real experience in, so far).
A BS in Physics was my primary degree (I double majored so I also had a BA in a language that has never been of any professional use to me).
Python is so ubiquitous that it's a great tool to know for a multitude of applications, and it pairs well with a physics background since that increases your usefulness as a generalist.
It is important to make the distinction between a programmer with a hard science/math degree and one with a computer science degree. The former will likely struggle more with building up larger libraries, following best practices for modularity/extendability/backwards compatibility, and other computer science sort of stuff that the latter will ingrain much better. The flip side is that computer science tends to not have as much of an emphasis on a math background, so analysis and Data Science applications often benefit more from the science/math background than the comp sci one (please note that I'm making highly generalized statements here based on what I've observed).
To summarize, if you want to build an app to do something, you want comp sci, but if you want to build a statistical model and have the ability to rigorously validate it and explain what it's doing, you're going to need that math background.