Trust me, I want a Server Browser, I just don't think they will go that route because of how they have employed their backend infrastructure. It would come with a whole slew of technical challenges that I don't think they are willing to commit to.
Back in previous titles, there were dedicated EA Servers, physical servers, hosting the games. They are now fully in AWS. So every round is a new server instance spun up virtually. At the end of the round, that thing is gone.
They definitely need to do something, because there is zero continuity between rounds. They are all just random messes right now.