I haven't heard of anyone getting the boot post 9/11. Pre, there was one or two cases where an instructor would stick around until they hit 1500 hours or more, in a market where you could get a job with 750 hours, so then they would be 'nudged' onwards. Now that doesn't happen though.
As far as 'how often and how easy we get jobs';
It's 'easy' to get a job with a background as an ATP instructor. The two main factors are A) You get a lot of hours per month, and B) 95% of those, if not more, are multi engine hours. Especially the latter there seems to tickle the airlines' fancy.
When it comes to being hired by a regional after you've worked as an instructor my impression is that it doesn't matter what name it says on your resume, who you've worked for; what matters is how many hours you have, and how many multi engine hours you have.
As such, ATP is a very nice place to start your career from.
Cheers,
Helge