I was noticing that most people don't really use Team up and often when people check team up for people, there are not people in team up. Its usually better off switching to a highly populated realm so I had an idea. Why allow players to have a setting in which they can autoregister in team up just by walking close to it and then there is a lamp next to each sigil in game saying how many people are in team up with a visible number.
I'm not sure about the auto sign up. I think many people have stopped using the feature because of shenanigans, such as a high probability of getting a bad team (like Tartarus when people are quick to abandon you, or Loremaster when you might get a junk team of low-level opportunists).
The people Team-Up hurts most are parties of 2 who just want extra help. In more popular dungeons, 2-member teams get split up when one joins a group of 3 and the other is left out to dry. If anything, people need an improved interface resembling Practice PvP window, showing you multiple queues, and displaying every player's level and school before you join.
Fixed Point players can view or check to show the number of players in que; as the OP suggested
Be able to select multiple Team Up Areas from a drop down menu
When a team is full, a player receives a notification they can respond to in so many seconds, where they can either select to go now, or give up their spot to the person next in que. And they get automatically dropped further back in the que for the next available spot; and so-on.