That definitely doesn't sound right. I'm working from iPad to PC and the Vector line is still fully editable on the desktop version of Illustrator.
As we don't have the Send to Illustrator option I'm going to assume you use the following process to export. Select Publish and export, choose AI, upload to somewhere in your Creative Cloud. Then open Illustrator on your MacBook, go to cloud documents and open the file.
This is the process I use to get from iPad Ai to Desktop Ai.
If you're doing something different, try the above and see if that gives you an editable Vector in an Ai file on your MacBook.
I'm not sure why you would want to go to all the trouble of exporting in another non-AI format just to re-open in AI on the desktop.
If you go to "cloud documents" in the desktop version, you'll see all the AI iPad files you've been working on, and you can open them directly without any conversion or exporting required. Then, you can re-open them on the iPad again later, trading the work back and forth as it is convenient (or as the work to be done may require).