You need to make apples to apples comparisons.
Being able to stash more players on the IR means more players who are not out for the whole season but stashed on IR while other players are then added to the regular roster. That means, even as the identities of the players might change, the total number of players employed by each team still goes up, which means total payroll goes up.
This really shouldn't be that hard.
If regular roster is X, IR players are Y, and PS players are Z, then adding to the quantity Y means more players on payroll, which either means increasing the salary cap or spreading the existing pot among more players.
You have 53 players on the roster, and 10 on the practice squad. The practice squad players make $6,300 a week, while the average NFL salary is about $2.5 million.
roster: 53 x $2.5 million = $132.5 million
PS: 10 x $6,300/wk x 18 weeks = $1.1 million
TOTAL: $133.6 million (give or take a few)
Scenario 1: Current IR
Player X gets put on the IR in week one, a 10-week injury, but, well, because it's the IR, he's done for the year. You still pay him his $2.5 million, but now you need to fill the spot he vacates on the active roster. You sign a replacement player for league minimum (~$500k). Bumping your total payroll up to $134.1 million. Or you move a guy up from the PS but now need to pay him league minimum, so he's making $500k anyway, and you add another guy to the PS, whereupon he gets his $6,300 a week. Either way, you're adding another person at, say, league minimum, to your team's payroll.
Scenario 2: Disabled List
Player X gets put on the DL, and you need to pay him. You need to fill the role, so you add a free agent, just like you would have in the first scenario. Pay that guy league minimum ($500k). Then, 10 weeks later, player X is ready, and comes off the DL. And you cut the replacement player.
How is the total payroll cost not the same in scenario 2?