It is quite rare in the current climate. Unfortunately, airports have their choice of a pool of self sponsorers to choose from, so therefore generally don't pay out all that money to sponsor somebody themselves...
I am one of the 'self-sponsoring trainees' you mentioned. It costs an absolute arm and a leg (best part of £20,000 for basic training and ADI rating) and even then theres no guarantee of a job.
However, if its something you really want to do, it is a way of getting your 'nose in'. It obviously involves a hell of a lot of hard work, initiative and debt, but ultimately at the end of it the plan is you will be doing one of the best jobs in the world...
If you need any further information just give me a PM.
Best of luck.
SS10