The only drawback I have found using the Note 9, and as my primary phone, is that it may not fit the RC holder if you have it in a case. Mine is in a case, and while it fits tightly its a little tilted...BUT the Note 9 is a substantialy larger device to begin with.
As for app opperation. I have had zero issues using a SM-N960U (USA Verizon)
The charging the phone while using the drone issue.
Yes, the controller does that. My undertanding is its an Android side issue, as Apple devices do not do this, not a DJI side issue. Regardless, I have never had a power issue with the controller/phone. I do make sure the phone is charged when I fly, but that is a personal choice I make and neither the battery levels in the phone or controller have ever been low enough after flight to make me think it would be a power requirment.
Overall I have had zero issues with the function of the Note 9.