Privacy On Phone

Unfortunately, “rooted” sometimes means user has super user powers, sometimes means (poor usage IMO) installing a custom ROM. IDK which you mean, but assumed the second. To improve a standard, vendor OS significantly is not feasible IMO, because you will likely disable so much, you break things you want to work.

Edit: This recent post describes a four fold path some have taken: Difficulty for dunce to setup an account to download F-Droid apk - #13 by TheLastProject