I just finished the video game and I gotta tell ya, I love this! I'd love to see you keep working on it, not just more calls, but also more character advancement (improving stats over time, or acquiring new Powers / ways of using their existing Powers, like the Hero Training sessions in the game).
I'm with max_expectral on incorporating "plot" between shifts and fleshing out the social interactions with the team outside of the dispatching mini-game. To *really* emulate the game, force players to take sides in disputes and manage who is pissed off at you or who is your best friend even outside of work, etc.
What's nice is that the format really does permit this to be a great solo RPG as easily as it does the round-robin group format - some additional random tables would really help lean into supporting solo play as well!