True, much of math is relegated to experts. This is _exactly_ the problem. Why do you think so many adults have such little understanding of math and will proudly proclaim that they haven't used algebra or geometry in their adult life?
Yes, there are are some areas of mathematics that are extremely specific and do require experts but a lot of math is useful to people in general and anything we do to make it easier for a new person to learn is something that will help the average person use it and will also make it easier for new people to enter the field.
The problem is that you can't really "think mathematically" without concise notation. Your brain won't hold the ideas.
The more that you get to stuff that you juggle around, the more that conciseness matters. So an important concept like "eigenvector" can have a lengthy name, but your vector is v, linear transform is T and the matrix representing the transform is M. Any other choice is actively harmful.
Making mathematics accessible to the general public isn't part of mathematicians' jobs, nor is it something most of them care about.
If you want to write some articles that make mathematics more accessible to the general public, and you want to use longer variable names in order to do that, nobody is going to stop you. It's unreasonable, however, to expect mathematicians to try to do this at the same time they're doing their actual jobs.
There is job security in keeping it arcane. Lawyers know that, too. But, since some professional mathematicians teach and others need to communicate with business people, you'd figure there might be some interest.
Yes, there are are some areas of mathematics that are extremely specific and do require experts but a lot of math is useful to people in general and anything we do to make it easier for a new person to learn is something that will help the average person use it and will also make it easier for new people to enter the field.