I'm not sure where you're getting the idea that more relievers would get hurt. If anything, this expectation that guys be ready to throw 25 max-effort pitches multiple times per week (plus however many times they're warmed up and not used) is worse. There were 38 pitchers last season with 70 or more appearances, 8 with 75 or more. In 2017, there were 32. Of those 32, 8 also had 75 or more. That level of usage ruins guys.
Of those 8 who made 75 or more appearances in 2017, six of the 8 spent time on the disabled list in 2018. In 2018, their ERAs were as follows: 4.45, 5.93, 3.22, 4.50, 3.58, 6.00, 4.85, 6.26. None of them exceeded 4 in 2017 (which of course partly explains their heavy use). The 3.22 is a LOOGY and the 3.58 was coming off a 1.78 season in 2017.
If managers can't manage with the expectation that they can use 4 or 5 different relievers every day, they'll adjust the usage patterns back to what it used to be: longer stints less often.
Or relievers will become even more disposable (which I’m not sure the owners would mind too much); I don’t see much changing with usage other than more guys getting called up when the current crop hit the DL
