No, we wouldn't.
If Player X refuses to ever play for Saints ever again, then we lose more money if we have to pay him for only 1 year than if we have to pay them for another 4 years. So the more they are owed, the more badly we need to sell.
Furthermore, if Player X is on a long term deal at high wages he is worth LESS to other clubs because he will not agree to terms unless the contract is an improvement on his current one. All other things being equal, would you rather have the player who is currently on 25k a week, or the player who is on 60k a week? You have a lot more leverage in the first instance so you would be more willing to pay a higher transfer fee and make up the difference by paying the player less.
The only reason why a long term contract would be worth more than a short term contract is if you have some ability to actually enforce it.
We can charge Man U money because there is a threat that we could potentially get Fonte in line and he will play another good year for us. Otherwise, we should just transfer him for free, because at least then we aren't paying him 50k a week to not play.
So people need to stop saying we are helpless to stop players who want to go. It's not the case. We have some limited ability to keep them here. And then it's just a question of whether it is worth it. But the contract isn't totally worthless. It's not worth a whole lot, but it's not worthless.
Speaking of just handing out rolling year to year contracts-- when you are redoing contracts for a player after every season, that's pretty much what you're doing.