They have been getting most of those innings from Sammons, Maeda and Hurter, they just haven't started. I think Hinch figures if he doesn't announce who the starter is, teams have to prepare for multiple possibilities. So far, it's working.
Possible but not really a concern this year. Rogers, Mize and Skubal are the only arbitration eligible players this off season. The end of next year might be more of a roster crunch.
https://blogs.fangraphs.com/river-ryan-jazz-chisholm-and-baseballs-most-injured-teams/
Fangraphs disagrees with our assessment of what the Tigers have lost to injury. Less than three WAR. Third lowest in MLB. Zips may not be the best at assessing young players though.