That's an interesting suggestion.
The calculation, though, is surprisingly complex. Even in a single-round tournament, it depends upon how many people sign up (which may be less than the maximum specified). People can drop out before the start. Also, the TD can also alter parameters before the tournament starts: changing from two games per opponent serially - to two games in parallel.
In a multi-round tourney, things get a little weirder, as the number of games depends on the number of people going through (which may increase if there are ties).
One of the issues that plagues tournaments is that a start date of "ASAP" can be a long way away.
I would like to make a suggestion as a site feature, but before that please let me explain why.
I enjoy playing tournaments and group team matches. Couple weeks ago around Christmas most of my games were completed and I wanted to start new ones. I enrolled few of them, but unfortunately none of them started sooner. I was planing to keep playing chess in the holiday season, so I kept enrolling different tournaments, hoping some of them would start soon. That obviously was a mistake. I ended up biting more than I can chew. Starting more games than I can give my time for (I usually play 1 day time control games) my performance dropped, and playing the games became for of a hassle than fun.
My suggestion is having an indicator giving the number of games that are about to start, just like games in progress. Therefore if the player ends up with too many games waiting to start like I did, they can notice it and disenroll from the some of the tournaments, or group games before they begin.
I know this is not a major problem, but it can be a nice add-on to the site, and useful for the players in the future.
Thank You
Hermes