Airlines provide training, but they also have other mechanisms to tie you to their company like benefits, pensions (harhar) and seniority.
Every ad for a corporate gig I have run across states the type rating and hours in type required for the job.
There may have been times when companies were willing to train for the job, doesn't look like that is the case at this point. They may pay to move a committed employee to a different type, but I doubt that there are currently many opportunities where someone is willing to invest in a type for someone who walks off the street.
Wishful thinking seems to be the origin of the 'oh, all the good ones are paying for the type rating' concept.