I thought about this briefly when I was trying to come up with a bid value for Ohtani, and I think there is isn't an issue here. In Mendoza players assigned to pitching positions accrue hitting stats. If you go to your year-to-date stats, you'll in fact see Ohtani atop your hitting leaderboard with 13.84 XR/27.
As an aside, the automatic accrual of pitcher hitting stats is an important piece of balancing the value of AL and NL pitchers in a mixed league.
Edit: Meant to also add since there's no DH PA min, there's no real advantage to putting him at DH compared to SP/RP for getting hitting stats. This would change if he ever plays the field.