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You can save to your WebDAV using the standard file picker. Surely an app that exports to Dropbox also gives you a "Save As" dialog.

Except for every iOS app that integrates with Dropbox.

Very true, iOS doesn't give users control of their data. To me that's more of a reason to not use iOS rather than a reason not to use WebDAV.

"You shouldn't use Dropbox because WebDAV is better."

"Sure, but that doesn't work with my iPhone."

"You shouldn't use an iPhone either."

"WebDAV should be enough for everybody"