Everything has advantages and disadvantages. The advantage of what you propose is that you don't use up much future salary cap on players no longer under contract or you can more quickly move on from players without taking a big cap hit.
The disadvantage is that you use up more of the current cap on signing new players to bigger contracts, because you use up more of the current cap with each signing. That would mean signing less marquee free agents.
A lot of the same fans that complain about the cap management also start complaining about the Saints not signing enough big name free agents fast enough, the very minute free agency starts.