Learning how to dance ( any genre ) is not necessarily a direct passport to teaching.
There a lot of skill sets that need to be acquired.. If you are intent.. get some prof. training in the techniques of dance ( from a Qualif. prof )
Salsa is a niche market, and there are many out there, who profess to know their "stuff".. good and bad seem to survive ( I contend with this on a weekly basis )..As a full time occupation, I doubt you would survive... however.. if you are in a location that is void of dance instruction.. maybe.. salsa folk are fickle, and have little loyalty ( B/room is a much stronger base )
I have over 50yrs of Prof. experience, and it means little to most outside of my profession ( with some exceptions )..
I know how you feel. I also work in the sports world as a writer, but most recently have been getting involved with the cultural arts commission in town and volunteering to help with an upcoming dance event. I have also danced in several community-based shows, and that's always a good way to get an intro into the arts world taking place nearby. But it does not surprise me that you find an interest in both sports and the arts. They are quite similar in a lot of ways; more so than most people would think. I only moonlight as an instructor. So you are wise to not consider that as a full-time gig, especially at this time with current state of economy. Terence knows his stuff in that regard, as he is one of the most knowledgeable voices on this site.
If your looking at the business side of things and realizing you have experience in that arena to offer the cultural arts there are plenty of opportunities. For example, colleges, universities, start-ups, etc etc that have local community services that need someone with business experience that can address their respective unique business objectives. Local theater arts, etc. It certainly is something to explore.