I've heard hams asking others if they want to do private calls on the DMR network which isn't really what ham radio is about, its supposed to be public and open to licensed users, if a ham wants to have a private conversation over the DMR network then there are other forms of communication for that outside of the hobby.
Ya using a different TG on simplex isn't exactly private call, it's simply a different TG#. I have mixed feelings on that private call stuff, if I need to be "private" I pick up my phone and call someone. (or text). A couple of us, have messed with that on Simplex but honestly, like I said, if I need "private" I pick up the phone.
Using a different TG on simplex is akin to simply using a different simplex frequency that isn't commonly used. Anyone with that TG can obviously hear and join in (and we'd likely enjoy that) but it's just different than what is commonly used in the area. I don't think using private call on a repeater would be appropriate, especially a busier one. Would make it hard to know if the repeater was in use and just a mess for everyone.
The vast majority of people don't even know you can do DMR simplex. We have an event here a couple times a year here which is simplex only and there are frequencies on both 2 meters and 70cm involved. I remember the first year that all got started, people said "no DMR is Internet only" and no, it's simply a mode like SSB, FM or AM, and it's how people choose to use it that makes it go out over the internet. Internet stuff has been around a long time on ham radio. Echo link or IRLP did analog a long time on FM long before DMR became popular with ham radio. About 20 or so years ago, I remember an analog repeater I was involved in, and we had IRLP on that machine.
A few guys lately in my area are using All Star to link some lower profile 900 MHz repeaters together, and they're all analog (for now) we may throw a DMR into the mix on that, only time will tell.