Yes there is, though much more study is needed. First there is lots of evidence about high velocity and spin. This is much more prevalent in 1 inning outings than 2. There is also evidence that warming up without even entering a game repeatedly is bad for pitchers (almost as bad as an outing itself).
Longer outings do require longer rest, but going 2 innings means fewer relievers in a game and the pitcher is much more likely to get 2-3 days of rest.
The biggest factor is the incentivization of velocity and spin of course and the incentive is with the pitchers too in how they train. The solution to me is still to deaden the ball which lessens the swing and miss incentive. Let pitchers be less afraid of throwing strikes because HRs are harder to hit. Maybe limit the pitchers on the roster too which would force different usage patterns.
Here is the recent MLB study though it is much more conclusive on velocity and spin than reliever rest.
The Phillies are just a huge outlier here compared to the rest of MLB and we did have most of our relievers run down at some point. It is worth examining further. We had the fewest bullpen innings of any team (yes that meant there was less need for 2 inning outings) but were 20th out of 30 in ERA. That is not good and probably would have been worse without Duran.
