You are free to shop around if you aren't treated with respect.
Yes, in theory. And in practice, not exactly. The school has some leverage on you when you're halfway down your training. Jumping ship at that stage should be carefully weighed against the non-negligible effort required to have your history sent to the new school. And those intermediate exams are not uniform across schools. Lastly, why would your current school want to cooperate to make it a smooth transfer? I wouldn't assume that they'll put any effort into this. In my case, it is rather clear that the path of least resistance is just to stick around and bite the dust until I get my licence. It is quite clear however that they have lost a customer as I'll further train elsewhere.
One word of caution to financially uneducated students: schools are keen to have you "open an account with/for them" where you wire the money for your tuition. Be wary as to ask yourself who really stands to benefit from this. Is a discount being offered for providing funds upfront or is that simply part of the terms and conditions of the school? I have been harassed in the beginning to do so and refused firmly because a.) there was no financial incentive and b.) that would have been loss of leverage for me had things gone wrong. Just be wise and swipe your credit card each time.
A lot goes on behind the scenes to make sure that most times a suitable instructor, a suitable aircraft aircraft and a suitable time slot all line up.
Absolutely, and it is actually rather a good thing for flight schools that demand remains steady/strong amid adverse regulatory climate. And that is precisely where a fine orchestration will make the whole difference between a successful school and stalling one. Have a look at busy just-in-time supply chain for a good example to start with.
Personally, I would flip this around and make it mandatory for each regular student to provide and commit to a list of N dates suitable for them to take a lesson. The topics would be left open and determined at a later stage. That would a.) force them to plan ahead and have fixed points in their calendars, b.) enable the school to plan their resources with a more lead time and c.) make cancellations due to weather/maintenance trivial to manage by shifting to the next appointment. Special wishes for rebookings would be either a considered favour or just turned down if impossible to handle. Also: instruct who may. What's the point of the constraint of sticking to one single instructor? Isn't the point of going to a school to benefit from a wider range of experiences? It might look excessively rigid but I am fairly confident that both parties stand to benefit from this. Surely this must be a major improvement over the current zero visibility with which they're operating.
When it goes astray, flexibility from customers is always welcome and usually gets repaid in other ways down the line.
At your school, perhaps. Still, I'm not so sure about this. All I see is the time it takes to complete my licence getting unduly stretched in spite of being accommodative with them.
At the same time, new students arrive all the time. All C172s are booked out today to teach these new folks to fly straight and level at the expense of more senior students who are told to read up on theory while standing-by.