Welcome to the forums bodelco
Unfortunately I only have a few minutes to respond at the moment, but here are a couple of thoughts off the top of my head. On the whole I would agree with you – the student is, after all, the consumer, and should be free to mix and match as they see fit. If you were renovating/redecorating your house, you wouldn’t feel compelled to choose appliances, fixtures, furnishings, flooring, and wall treatments all from one merchant, so why treat the renovation of your dancing any differently?
That being said, however, a lot also depends on what you want out of your dancing. If its just a matter of fun and enjoyment, then absolutely – i.e., who cares if your red pillows clash with your green couch if you like it…its your house/your dancing after all! But, in the same way that an interior decorator can help provide an integrated design, so too with a coach. A primary coach can help integrate various elements that you have acquired through a variety of sources. Also, various coaches can sometimes end up being classified in different “camps” as it were, i.e., choreographers, technicians, performance coaches, etc. So, rather then having a rumba coach, a lot of couples choose to get rumba choreography from coach Q, while still training with coach R. I think this is more applicable to competitive dancing, but given different prioritizations between coaches, I think that it is important – at least for those who want to compete – to have a home coach. A home coach provides more consistent feedback over time, and also has a larger repertoire, gained via exposure, with which to assist – i.e. “you want the same sweeping effect there as you have in your fall away slip pivot in your waltz routine.”
Have to run, but I’ll check back in later.
--Jonathan