A manager can't really help it much if his starters are constantly failing to get to the fifth inning. Stack a few of those together, and no amount of effective bullpen management will avoid the crunch.
But a manager absolutely can control starter usage when they are pitching effectively, or at least aren't letting the game get away early. You don't know what the next few days will being you in terms of start length (especially with this rotation so far) so you need to squeeze whatever you can out of them when they're on to avoid using bullpen resources when you don't have to.
Not that he's had a lot of chances in this department so far this year, but I think Rocco has shown mixed results in this area. It's easy to imagine him pulling Lopez after 6 in his good start based on track record, but letting him take the 7th meant one less bullpen arm compromised going forward. On the other hand, I know Ober was about as sharp as a butter knife in his second start, but he was at 84 pitches with a 5 run lead going into the 5th. I think he should've sent him out instead of going to the bullpen there. Even if he doesn't finish the inning, you're giving yourself a chance to save one more arm going forward. But he didn't, and then Paddack does his thing the following day, and now you're relying on SWR to relieve the stress on your bullpen with no off days in sight. Not a good spot to be in.
And if we must keep Paddack around for the time being, can we at least get him away from SWR in the rotation? I'm starting to get Bundy-Archer vibes with that arrangement