That's the problem. The core players, who are highly paid. Those are the contracts which needs reconstructing. Too many of those reconstructed, and that guarantees that the player gets paid for the guaranteed portion.
The problem is injuries. We know that in our SB year, we had like 15 injured players on IR. No one knows who will get injured in the future, and it could be, that in any given year an inordinate number of players with reconstructed contracts will get injured. That's when it starts backfiring to the club. They are on the hook for $millions, potentially.
Example...W Smith, & R Harper. If their contracts are reconstructed, and they get injured, then even if the Saints want to get cut them, their money will still have to be paid in the future, which makes them almost immune to being cut.