In that situation I don't think charging more would go over well with consumers.
Have you seen this done?
Netflix offers in app purchases for streaming subscriptions if you pay through their games. But only the ad tier.
You can subscribe to YouTube or Hulu via in app subscriptions. But you can’t subscribe to YouTube TV or Hulu Live TV via the app.
I guess these days I would offer a higher month to month subscription through in app purchases and a lower yearly subscription from the web.