An attacker would have to trick a user into installing a malicious app, which unlike some malware wouldn’t require any special permissions.
The bad news, then, is that once the app is installed, it can gain full root access to the device without requesting permissions from the owner, but you’re not at risk if you stick to known apps installed directly from Google Play.
I've never seen an app get full root permissions on the phone without me explicitly giving it. How does that happen, maybe in recovery?