As to the question of whether there is enough demand for training to satisfy the supply, the OP doesn't have a sound enough understanding of what is actually happening in instructing.
I work at a well-known university 141 program in Ohio. I've been working here since 2013 and our instructional staff has COMPLETELY turned over (I'm the most senior instructor except for the Chief). We also are down from 20 instructors to 16. This is despite increased hiring activity and, for the first time in years, widespread interviewing of outside applicants. Additionally, student enrollment is higher than it's been since 2007. This is a typical story for flight training operations in our area. There is absolutely no way, in the short term, that we are going to work through this demand in a couple of months.
By the way, schools as far away as California have been calling offering to pay for a CFI's relocation costs and give them a signing bonus since they are in the same boat.
The primary causal factor is the airline hiring climate. Post-2008, many instructors were stuck in the CFI world until upwards of 3000 TT (which with Ohio weather can be a seven-year slog!). Today, the moment a CFI reaches R-ATP mins they have job offers from multiple airlines and are gone. The training supply is limited by the fact that all those "active" certificates are actually turning into airline pilots much faster than in the past many years.