Another reason for the 7 day limit is people subscribing with a normal subscription, then going offline with their Switch, and then cancel the subscription.
If they keep their Switch offline the Switch knows no better than that the subscription is still active. Since there is no way of knowing whether the subscription is still active when the system is offline for a extended period they need to block certain offline services that only come with the subscription at some point until you get back online.
It's quite understandable really, and in practise for the user there's no issue at all since anyone can get online at some point during the week.. You'd have to try hard to go a week without the possibility of getting to a free WiFi hotspot.. And in those cases I'd say you probably have other things on your mind.
As for Cloud backup, I agree a "grace period" is nice for the consumer. And I still think that there might be a short period of a few days or even a week. However, since the days of a new subscription get added to the remaining days of your previous subscription when you renew, the smart thing to do is resubscribe in the weeks before your subscription ends.
There's also automatic renewal so if you want to be completely sure you should keep that on.
Also, remember it's a backup. Not a main form of storage. You should always keep save data you don't want to lose on your system as well.