They rolled out something on a few minor regions back in April, ran into issues with queue times being broken. Then PBE had a similar issue with queues being broken with the new TFT set.
If I had to guess, I think Quickplay is delayed because there's something messed up with queues in the backend, and they need to solve that first.
We fixed the issues with the matchmaking test within a day of launching, the results were really positive after that. We were hoping to get Quick Play out before the midyear patch but weren't quite able to finish before we had to pivot to Emerald and other ranked Split 2 stuff, so we'll be picking it back up shortly and plan to get it out later this year.