you posted evidence that some bench bats get paid, not that additional bench bats will get paid. The three batter minimum eliminates the loogy - guys who can make two or three times league minimum. In exchange, you grow the bench.
I think we're discussing two separate changes. (1) 3-batter minimum: likely eliminates LOOGYs, but they are more likely to be replaced with another pitcher (on a min salary) than another player. (2) limiting pitchers on rosters
may shift balance towards position players, but it's likely trading off a bullpen arm near minimum for a position player, likely also near minimum.
If the issue is simply LOOGYs and you're Clark, you have to look at the thing overall: you're getting an extra roster spot (2 minimum salaries at worst) in exchange for eliminating the LOOGY, guys who more often than not are on minimum salaries as well. By my count, there are only 4 (possibly 5) LOOGYs for this year on contracts more than $1.5 million, and most of them are paid like that because they're good enough to also get out righties. That's not a lot of money to risk leaving on the table in exchange for 30 extra jobs.
As for my post, the point was that guys like Descalso, who are almost paradigmatic 25th men, are getting significantly above minimum. Not always, but sometimes. This evidence suggests that for at least some teams, they'd add a 26th man above minimum. There's really no way to know, but there's a decent gap there. It doesn't really matter.
