This type functionality has been requested a number of times for the Game Schedules plugin, but this is the first time for the Team Rosters. (Except for requests for baseball and hiding the weight for women's teams.) If you read thru the Game Schedules threads, you will see the following issues:
1. I did not (and still do not) intend to build a general purpose table widget. A number of them are available, some very good. However my non-technical, volunteer users have been frustrated by the difficulty in using them. (I think they are pretty easy to use, but perhaps a bit tedious.)
2. There always seems to be a trade to be made between general-purpose (flexible or highly configurable) and ease of use. I've consistently tried to favor ease of use and simplicity (not that I've always succeeded.)
Some more technical users have gone in and hacked the code to delete columns and/or re-purpose existing columns could serve their purposes. Others have created translations of the headers to made-up languages, which works pretty well.
I am very open to ideas on how to maintain the simplicity while increasing functionality, as well as providing better support for WP Multi-Site. I'll think about your ideas.