I think flash photography at sporting events is doable. I know I have successfully gotten away with many times in my career. It's not a distracting as some people on here make it out to be if done right.
First of all, a SB 800 (which I use an example because it's in my bag) has a pretty powerful flash that can reach out 40-50 feet if needed (which sometimes during sporting events is all you need). Next, if the field has lighting on it already most of the time a flash burst isn't that distracting to players who are in the middle of their game and aren't paying attention to the sideline. If the field is dark, this might not be as true.
I often use strobes during night sports just to add a little fill light on subjects. I have had a coach or two complain but for the most part, I would say 90 percent of the time, nobody says anything at all.
But, as already stated, the best solution is to get a high ISO body and fast glass. That is the first, and most crucial, step to shooting good sports photography at night.
I'm guessing that you are shooting high school sports. If you had a coach or two complain then that is one or two too many complaints. These events are about the sports, the players and the teams, not the photography. A sports photographer should NEVER even be noticed when they are shooting an event.