Having done both Pro/Am and Am, I'd say that in my experience it's virtually impossible to just "practice" with one's teacher. My ex Pro/Am teacher used to tell me that he felt he had to constantly give me information or else he'd feel like he wasn't doing his job -- that I had paid for his expertise and he felt he'd better give me 45 minutes of information or else he hadn't earned his paycheck.
This, of course, meant that corrections and improvements and new information were always coming at me. I got good at automatically sorting them into "this is what I have to do right this second", "this is what I have to do this month" and "this is what I'm aiming for over the next few months." Still, it basically gave me no time to really think and experiment.
When I was a newer dancer (Bronze & Silver), practicing on my own really helped a lot because it gave me time alone with my thoughts to try things. But after a while all the corrections I was getting were related to how I dance with another person present, so I ended up with even LESS time to personally sort through the information I was getting. It got very frustrating.
Now that I've got an amateur partner to work with who is on the same wavelength with regards to learning, approach to technique, etc, it's a whole different world. We take a lesson, and then we can spend the next week sorting out what was said and what it all means and how we can produce the desired effects together. I've learned more about following in the past few weeks than I have in the past few years of Pro/Am, and I attribute it to just having the 'quiet time' to really get to "listen" (feel) what my partner is doing, and to experiment and see how I affect things. It's pretty incredible
I really think my time doing Pro/Am was extremely valuable in that it gave me a strong foundation and also gave me a chance to learn and intellectually understand a lot of important concepts. But for me I got to the point where I needed to be cut loose and see what I could make of my dancing without being in the presence of a teacher every time I danced. My old Pro/Am teacher and I talked once about how Pro/Am was grand but it was sort of like having training wheels, and that at some point the wheels had to come off. Now, I'm not saying every Pro/Am relationship is like this, but mine was, mostly for the better but sometimes for the worse. I strongly doubt I could be as strong and as thoughtful (regarding dance concepts) a partner as I am now without the training I received in Pro/Am. But I also know that I'd never have started thinking about the artistic side of dancing without having gotten out from under the caring wing of my Pro/Am teacher.
As usual, your experience may vary, I'm just relating what I've experienced....