I've thought about this a lot over the years. I currently sell two basic product types on my theme shop: individual themes and a theme bundle, both with automatic yearly renewals for support and updates.
I've noticed many of my "individual theme" customers immediately cancel their subscriptions. And honestly, I don't blame them. Once the theme is released, I don't make any substantial updates. A bug fix here and there. Integrating a new core feature (or migrating one previously in Jetpack, like Site Logo). The theme is always at least 90% functional as it will ever be on the initial release.
The annual theme club subscriptions, however, haven't seen a single cancellation yet. Not that I'm expecting that to always remain the case, but at this point, I can definitively say that theme club memberships will always be more consistent than individual theme support subscriptions.
I've totally ruled out monthly subscriptions, for a reason you touched on: churn.
It wouldn't make sense for an individual theme subscription, unless it was some gigantic framework (a type of theme I have no interest in making) that I was constantly adding features to. It might make sense for a theme club, but then you'd be pressured to release a new themes on a monthly basis. WooThemes used to do this, and they didn't do it for long. It's tough to consistently make new hit themes every month. It was a bit more common in the Joomla community, although I'm not up to speed on that any more.
When a couple months pass without any theme updates or support requests, the customer is going wonder if a monthly subscription is really necessary. It's like maintaining a Netflix account when you know you won't have time to watch anything. What's the point of continuing? You might as well be flushing that monthly subscription money down the toilet, and become much more likely to cancel.
The only time a monthly subscription might make sense would be if hosting was bundled too. Something you can set up with a company like Pressed. And even then, there's a reason why every single hosting company offers a discount if you pre-pay annually. They'd rather get that cash upfront and not have to worry about the customer cancelling a few months down the road, which would result in significantly less revenue.
At that point, it's just an exercise of money management. When you get a yearly customer, and you spend the entire cash infusion in one month, you're going to have problems later on. Internally, it's best if you just "pretend" it's a monthly subscription. Ideally, only after the refund window has closed.
In any case, I'd be hesitant to include monthly plans as an option at all.
Limiting support and updates to those with active subscriptions is always fair game, but I'd avoid any needless "crippling" out of principle, even if it's just on the backend. Although I admit it would probably be a good way to encourage renewals, you can get a similar effect with automatic renewals without the negative reinforcement.
Another idea I had would be to start a theme club, but only include themes released after the customer signed up. Any backdated themes would have to be purchased separately. I don't think I'd do this, and not even sure how to make it happen considering current ecommerce plugins available. Just an idea to encourage people to maintain their subscription (i.e. if the subscription is cancelled, they'd have to "start over").