Jeffers has played in all but six games and is third on the team in plate appearances. Realistically, catching Jeffers more wouldn't get him the lineup more. He would just DH less. Said another way, Vazquez isn't costing Jeffers at bats; he's costing at bats to someone else in the lineup as the DH.
And frankly, the "someone else" crew hasn't hit well. The DH tOPS+ is 85, meaning that they have hit 15 percent worse than the team as a whole. For context, the only position that has been weaker is 2B (at 82). Then, consider that more than one-third of the DH at bats have gone to Jeffers, and it suggests that the remaining DHs have been significantly worse than that figure. Not Vazquez-level worse, but with not nearly as large of a discrepancy as one might think.
In fact, given the toll that catching takes, one wonders if Jeffers might actually have fewer total at bats if a bigger percentage of them came at catcher.
It will be interesting to see if there is some shift in the catching ratio, with Larnach seeming to be coming on a bit as a DH and if Lewis (hoped for) leads to more DH time for Miranda. If those guys hit well as DH, maybe there's more reason to have Jeffers catch a bit more, since his DH at bats are needed quite as much.
Rocco plays the long game during the regular season. If part of balancing the role and giving lots of DH time to Jeffers is to keep his legs a bit fresher so he can catch a little more down the stretch, that's helpful as well.