Stuff like this is why I try to avoid apps that operate their own syncing services. If Vesper had used some kind of file format you could just keep in your Dropbox, and used that for syncing, all the developers would need to do is stop paying for the proprietary font in order to have zero operating costs.
Obviously you can't avoid all problems this way (Apple and Google and Dropbox sometimes change their APIs, or discontinue them, e.g. Google Reader), but it goes a long way to building confidence that even if the company fails, people can continue to use the app.
At the time Vesper was written, iCloud sync was not reliable. It's gotten better (good enough for many apps to proudly use it), but by that point Vesper had lost its dev.
There had also been issues around this time with Dropbox changing the way the SDK presented information. A small change, but one that ran afoul of Apple's In-App Purchases guidelines. Debate the merits of the conflict all you want; it was still an issue everyone wanted to avoid at the time.
Basically, you're not wrong, but I believe the devs made the best decision they could at the time they wrote the app.
You could use the Dropbox API with oauth. The same files in Dropbox can be used to sync the web API, phone apps, and desktop apps.
You could also roll your own solution with S3 or something like that. The point is that you will be using fairly common and popular services which aren't likely to go away anytime soon, and aren't operated and maintained by yourself.
You could also take the approach 1Password does: operate your own sync service, but allow users to use Dropbox or iCloud instead. The onus is on them to make sure the files are in the right places, but they effectively have total control over the files, which a lot of people like.
An alternative to look at is the Couchbase Mobile stack. The stack in includes the Couchbase Lite database (NoSQL), Sync Gateway, which enables syncing and more, and Couchbase Server. All open source. It's pretty easy to run all yourself, or on something like AWS. The db runs on many platforms, both mobile and desktop.
Obviously you can't avoid all problems this way (Apple and Google and Dropbox sometimes change their APIs, or discontinue them, e.g. Google Reader), but it goes a long way to building confidence that even if the company fails, people can continue to use the app.