Division by zero can certainly be given meaning in other mathematical contexts. The real projective line is one example [0]. There are other algebraic structure

Division by zero can certainly be given meaning in other mathematical contexts. The real projective line is one example [0]. There are other algebraic structures in ring theory that also have a division by zero, for example a ring with only a zero element. So I would say it depends on your context if something makes sense to do. You aren't ignoring or doing something ill defined, its the opposite (in mathematics). You can do it if its consistent mathematics. Physicists have very good intuition but sometimes making their statements mathematically rigorous requires extra work. I think a good example is in the history of field theory. Over time the intuition was made into something more formal. The article in the OP discusses renormalisation. [0] https://en.wikipedia.org/wiki/Projectively_extended_real_line https://en.wikipedia.org/wiki/Projectively_extended_real_lin...