Right now you get problems like Tweetbot. It costs money to maintain Tweetbot and keep it working, and to add new features. I use it every day, I'd be happy to 'subscribe' to it.
As it is now they only get paid when I buy the app. If I keep using it for 4 years I may still expect support but they're not getting additional income.
If you don't have enough growth to sustain you, what people have to do is release a new version of the app. Maybe it's a big upgrade (like Tweetbot has done) but some companies basically arbitrarily decide "This one is new, pay again".
And even though Tweetbot is great they lose money because people who are addicted to the app don't want to pay another $2. And they spam the rating for the app with 1-star ratings.
For apps that need constant maintenance? This seems like a great idea.
This is like leasing vs buying, the only difference is with your example you'll get one choice, pay the lease, or pound dirt. I'd rather buy the app once and be done, and have the choice to upgrade at my discretion, than be forced to pay yearly.
If Twitter changes the API on Monday, how many versions back should Tweetbot have to support based on a single $2 (or whatever) a few years ago?
That's the issue. People get pissed there isn't perma-support for apps that need constant updates. This is a way to make that more feasible.
The only difference is that Google makes it easy for people to abuse the system.