I have to congratulate Billy whu for one of the most balanced posts on the subject that I have seen on these forums for a long time.
The big problem is that the integrated suppliers are not just working for you when they place you with an airline, the airline is giving then a kickback for supplying you to them.
Airlines have been selling the young and aspiring right hand seats in just the same way as they sell the seats down the back, the advantage of integrated pilots is that the airlines get pilots of a set standard to work with, it is not that they are better than modular pilots ( in a lot of cases they are very narrow in understanding of airline operations). This makes the integrated student the Human resorces departments flavor of the month but as the HR business is only as good as its latest fad this could change overnight.
Having worked for eight airlines the best of them recruited using an interview with a management pilot and a sim check, the worst of them had HR doing the recruting and at the interview asking all sorts of stupid questions and of course the mandatory tests that equire about your liking for otters and other abstract consepts, the result always seemed to be a very unhappy place to work.
The last thing I would warn about is integrated suppliers who go out of business and then start up with almost the same name out of the same building using the same aircraft having left a trail of unpaid debts behind them, they will take your money and run in a heartbeat if they think they can get away with it.