I agree here. I have used Origin for 11 years, and never had any real issues with it.
Like you said, shelve EA App until the feature level is on par with Origin, as someone who is playing a lot of older multiplayers (DAI and ME3), not being able to invite/join from the friends list is a huge step backwards.
My solution: Do not force the EA App on people until it is truly ready. As of now, it feels like it is a bootable alpha (or beta build in the best case)
Here's my issues so far:
1. Not being able to join or invite people through the friends list - MAJOR LETDOWN.
2. Multiple in-game issues related to "Origin not being present"
3. In-game overlay does not work at all
4. Friends list is bugged (does not show all my friends)