If they would, they would very fast hit the point of diminishing returns for their investment, or straight-up big losses. That's not a successful way of running a business. They would have to find the perfect price where the team they want to poach the player from would agree monetarily and the point where the player wouldn't be hugely overpaid. That price is hard to find.
Trades would be the most logical way to get the desired effect eg. if they got blameF from coL and send back nitr0, I could see it work.