The downside of this is that they have essentially limited themselves to a single aircraft and therefore a smaller number of jobs.
Ok this is not entirely true.
You do not limit yourself but you do qualify yourself on the particuliar type.
Offcourse you are feel to go there where you can be hired to fly a different type.
Cost is the issue.
If you can afford to self sponsor a rating and you have no problem with that, then why not do it?
You can always continue to apply for other jobs, only thing is to bear in mind that you might have to pay upfront a second rating, but this one gets you the first job.
Lufthansa Cityline is a great chance, once hired there, you are entitled to a sum of cash to compensate you for your own funded training.
Don't know if there are other companies who do that too.
If you did have to pay for one yourself how much would it cost and would you only have to pay for one yourself when you have landed a job.
Cost is different. Lots of places to start training. Check out the adverts here around the forum pages.