Of the three pokemon, Ivysaur is easily the worst, especially when it comes to match-ups, so as a result most competitive brawlers would prefer to skip her. Squirtle and Charizard are 80% of the time more effective in getting the job done.
I'm not saying Ivysaur is bad. Personally, I like Ivysaur and I try to use all three equally. But sometimes risking Ivysaur in matches were Squirtle and Charizard own is not worth it.