[jacobolus]

It is intuitive and easier in the sense that when you don’t have that vocabulary and bag of concepts – trying to work in some other formalism – all of your arguments end up being much more complicated and cluttered.

As for the number of scalar parameters involved: if anyone wanted to put significant time and money in, as has been done with matrix computation libraries, most of the 0×0 multiplications can be skipped, and the rest can be efficiently SIMDized, etc.

If the concern is bandwidth over the wire, there are often ways to compress things. E.g. we can take the stereographic projection of a rotor and then reduce the precision to save a lot of I/O without losing accuracy.