It is just a matter of using a bit of time on collecting the figures, they seem to be available if you just call your local CAA.
I don't think that the flight schools will have no one to train, but they would have less to train if people really understood the job-situation that follows when you finish flight training. And that is only fair, in my opinion, since today they train much more people than needed.
When people have invested time and money in a professional flying certificate, they are very dedicated to getting all the way to a job. This means paying more money for type ratings, FI ratings, line training etc on their way.
In the end there is not a job for everyone and the ones who did not get a job will have lost a lot of money and that's a shame. It would be alright if it was just a small percentage of people finishing flight training, that would in some way be natural. But in this industry it seems to be a very big percentage who ends up having to find another career.
Again it is hard to say for sure when there is no data available to judge from. You can only judge from your personal experience. That is what everybody do and even though they are often right when complaining about the missing jobs, it's a little hard to base any decisions on. Specially if your are new to the game.
Some real numbers and figures collected from the CAA's and other reliable sources would make a big difference.