The two starters were reclamation projects, one of the SPs had serious elbow concerns prior to the trade, and the other isn't a stranger to the IL? Wasn't relying on the young arms the plan all along?
I doubt many of us were expecting Bundy and/or Archer to last in the rotation so that seems like an obvious "count on the minors," move. Paddack was a gamble, and we can argue about how calculated it was, but his elbow issue didn't sneak up on the Twins. Gray making an IL shouldn't be all that surprising. Winder was shut down with shoulder issues at the end of last season. Ober has struggled to stay consistently healthy going all the way back to his college days. Ryan is the only one I can really look at and think it's just plain bad luck.
It's a bummer that the injuries have clustered, and maybe that's the real issue, but looking at them on a case by case basis none of them should be all that shocking. There were plenty of us prior to the season, yourself included I believe, that questioned where some of these innings were going to come from based on staff construction.