There is no easy answer...
It is true that along the years, CAE and L3 have graduated many pilots and they could now be in key recruitment positions
On the other hand, my student graduates tell me that application forms don’t ask from where you got your licence
If you want to transfer to a different ATO, there are plenty where you will start flying immediately...
btw, it was publicly announced that L3 put his entire pilot training división for sale... and I believe he already sold it... except the basic pilot training part of it. Google it for confirmation