Maybe - but a big golden-hello, a couple of reasonably well paid years, experience, training and CV padding is as good a reason as any. Just like any other job.
It would be nice to think all people do their job for the greater good and to sincerely put others and their interests first. That bankers really want to help you save money, that the salesman doesn't just care about commission, that the police only care about upholding the law and job center staff all only do it because they truly, deeply, really care about their clients. But we all know that's BS, and 'doing it for the right reason' is something teachers certainly don't have a monopoly on.
A wage and progression are the reason most people do their job.
And Teach First, if i didn't have something better to do, sounds like quiet a good deal.
That said, whoever said they'd feel like having failed if they took up teaching...grow the F up.
And getting a maths PHD will not mean you'll wake up in the morning with the city of London camped on your doorstep and you'll be able to pick at your leisure over breakfast. Yes, you'll have the prerequisites...but they do not a job offer make...