Is “spend salary, save bonus” actually a common strategy?

Most people save more than that - that is just a catchy phrase that gets the point across that you shouldn't spend money that you haven't received yet and may end up not receiving. 

have heard the phrase multiple times. Agree with the above, the adage is pretty old and comes from a time when base salaries were much lower relative to bonuses. Think with base salaries as high as they are today, people end up saving some of their base as well, whether on purpose or not.

Living in a LCOL city and doing this job, I can't spend all of the base if I tried

Manage your money as if you're not going to get a bonus, because you don't know if you're going to get it until it's sitting in your bank account.  Put a couple thousand aside every month in savings.  When your bonus hits, get something nice but not too crazy and put the rest into savings / investments.

I would advise saving a portion of your base salary every two weeks. It's never wise to live paycheck-to-paycheck unless forced to by circumstance.