You are making the same assumption as everybody else. That the players will always put money first above all else. Some will, but not all of them.
I'm talking specifically about Keane here, but the same principles can also apply to Klaassen.
The lad is clearly unhappy here. Every time I watch him he looks as though he is about to burst into tears. He's making a lot of mistakes and is getting slated for it by players and fans alike. Not sure I've ever seen Jags so animated as he was after Keane's blunder for the Porto goal. His skillset is not suited to the way Silva is likely to set up and he knows it. He knows that he will get very little game time under Silva.
Conversely his skillset is ideally suited to the way Burnley set up and he knows that Dyche will be happy to take him back if the price is right. He'll have to take a hit on the wages front but he can still expect to be on much more than he was when he left as he had run his contract down.
Burnley are in the market for a new defender. They are looking at both Mawson and Gibson, both of who would cost well over £20m. He could get Keane back, somebody he knows really well who fits his system, for probably as little as £15m. That's a £10m profit on the lad in 12 months which will more than cover the cost of his increased wages.
We have to take a hit on the transfer fee but it's worth it to get him off the books. I reckon Keane, and Klaassen for that matter, are both the type of character that will be prepared to take a a reduction in income if it means getting their careers back on track. Both players have also been dumped by their national teams whilst with us too which gives them extra incentive to leave. I might be wrong, but I wouldn't automatically take it for granted that they are purely motivated by money.
Now the likes of Williams and Mirallas, they're a different matter entirely. It will take salary subsidised loans to get them off the books this summer.