I guess I'm not understanding the issue. When a game starts, I can still put a transaction in involving a bench player can't I? Once games start for a day, nobody can add anyone till the next day, that's how it works. Just gives you the opportunity to add guys for the day before games (all games, not just the specific players game) start.
I could be wrong, but I'm not sure what your are concerned about is an issue.
Also, to be clear, I'm not suggesting this because of my stupid f***-up. Suggesting because I think it would be a legit improvement across the board. Like if a prospect gets called up with little press/notice, you could pick him up for that day. Same for a late DL assignment (or one you missed while having a real life).