After several months of trying, I finally found a TSA check-point where I was able to use my California
mobile driver's license a few days ago at LAX.
This seems to be a feature of the new facial-scanning TSA stations. They have a barcode/QR scanner not unlike the ones at boarding gates that you put your phone under with the mDL QR code showing. The app then came up with a prompt that someone was attempting to access my personal details, with an option to accept/decline their access. ie, it seems the QR code itself doesn't contain my details as such, but gives the system what it needs to contact the DMV who then ping my phone for approval before sharing.
At some point during the process I think there was a "look at the camera" prompt, although it actually took the photo before I even realized that was happening (I guess I just happened to be standing in the right spot at the time - not surprising given the QR code reader is directly below the camera/screen).
All up a smooth process, although not as easy as simply putting my physical DL into the slot which was the other option. I guess if I'd left my license at home it could be a good backup, except...
Technically this is actually the 2nd time I've found a check-point where I could use this. The first time was a few weeks ago at SJC - however a few days earlier I'd received a notification from the CA DMV Wallet app that my mDL had expired and needed to be refreshed - which requires the physical drivers license and takes a few minutes. As I hadn't done the refresh, I obviously didn't try using the mDL on that occasion. I don't know how frequently this happens (or whether it's based on straight time or how long since you've opened the app/etc), but to some extent it defeats the entire point of having a mDL if I need to refresh it using the physical drivers license at regular internals.