No. Lovren and Banega are like that, but I don't think Wanyama hated Celtic nor was Celtic broke. Clyne wasn't in that position, or Jay Rodriguez. Ramirez wasn't at the most stable club, but I don't think he hated it there. For those guys, they simply wanted to advance their careers and get that huge paycheck that would set them and their families up for life.
If those players had gone to a bigger club, they wouldn't be any closer to CL football than they are at Saints. They'd be putting their time in at the reserves and trying to fight for a first team position. If Saints don't progress with the player, then they'll leave. But if Saints do progress with them, they may stay.
Banega could easily be playing in CL at a huge club right now if he could get his act together. If he comes to Saints and puts in a half season of the kind of football he's capable of, he could well be off in January (at a huge profit to us, of course) to a powerhouse somewhere. We can't move as quickly as he potentially can.
Lovren's career has stalled out as well, but he is less proven, so his timetable could be similar to ours. But what Lovren and Banega need most is a change of scenery, not first team experience or finding the right club where they can get noticed. They are at Saints because they messed up at their old clubs. I don't think that's the case for our other signings.