Compensatory picks are a vital part of the equation due to the way things work currently. Resigning a player and signing a FA both carry the opportunity cost of a lost compensatory pick. We could have felt comfortable paying Sweezy exactly what he got from the Bucs and the right move would still have been to let him walk and collect the extra 2017 3rd round pick his loss contributed towards. The size of the contract they gave him just made that decision easier but he is probably the lineman that they would have liked to keep the most.
I also think you have to look at the situation around each player separately. Okung's decision to act as his own agent likely sunk any chance at resigning him given his injury history. Carpenter and Unger had both missed extensive time due to injuries while they were here. Giacomini was a personal foul magnet. Moffitt lost his drive, and I don't think anybody was arguing for extensions for guys like Schilling, Lem, Lewis, Bailey and Gilliam. We've also chased at least two OL in free agency that went elsewhere, most notably TJ Lang.
Those outcomes are perfectly reasonable for a team trying to spend it's money wisely and extend key players at a reasonable price. I don't agree that it's indicative of a team that is trying to go cheap at offensive line and I don't see a Britt resigning as a change in strategy.