The free app vectornator offers the option to simply open your work in progress artwork in illustrator.
You can simply tap a button in the app and if you sit at your computer, have the app and your desktop version of illustrator linked to the same adobe account, it will open up illustrator and open your artwork.
No exporting needed, no saving it to the cloud.
One click and it opens it up.
Something like this would be quite beneficial to work seamlessly between the two version.
Ideally you could also do the same in reverse, just click a button in the desktop version and it automatically sends your artwork to your app.