The two INTs definitely didn’t help Milroe’s case. But I think it’s more than just the INTs that led to Buchner being the starter.
It’s the inability to make even a decent defense (and UTw is far better than decent) respect the passing game. If they don’t at least respect the threat, they do what we saw Saturday night  load the box, deny the run, and mount an all-out attack on a jelling OL.
Milroe’s problem is that the classic counters to this  quick decisions on hot routes, checkdowns to short passes, ability to make even 2 reads in quick succession, etc.  are exactly what he has not mastered.
So no, the interceptions didn’t help. But I believe the lack of confidence that he can force a narrative different from the one that led to the INTs is what landed him on the pine.