As others mention there's alternative approaches. For someone with a physics background thoughm it's very natural to think of matrix - or rather tensor, i.e. more than two indices - operations with indices - it's how we work in (general) relativity and some condensed matter physics. So while obscurity depends on your background, it is sometimes a bit finicky - I can't count the number of times I switched indices around or wrote an 'i' instead of a 'j' but that's something that I deal with with testing (mostly property-tests in physics).

It's not optimal, but it's the best I know and named-indices would have their drawbacks too.