I mostly agree with you.
The connection to physics in the OP is apropos. Physics straddles the line between mathematical purity and empirical data, and sometimes you have to give up some elegance and do some hand waving to get stuff done in the real world.
Similarly, in programming we deal with real world events that hamper our ability to make assumptions, like BrowserUK's lift motor. I spend much more of my time defending against those events (customers entering VISA in the "name on card" field, customers putting URLs in the search box, etc.) than I do contemplating the lack of rigorous mathematical backing of my actions.
But, I don't feel like the study of "the algebra of programming" is useless to me, even if I don't care about it. As a physics major I really disliked mathematics but it provided me the tools to get the job done. As a programmer, do I care much about this subject? Not really, but I know that work in this direction will inform the tools I'll be using to program 20 years from now.