With three players, each participant's role is more valuable than with five.
As for the example with your team, I don't think it's representative. My team was one win short of the semi-finals, but I believe that everyone played as responsibly as possible, and the number of people on the team somehow didn't hinder us.
And Cobra is right: in a team tournament, you need to choose players not only based on skill but also on reliability. No matter what the replacement system is (and I'll think about how to organize it best before the start, perhaps we'll take a variant from Game of Thrones), any replacement will still weaken the team (it's important that the replacement doesn't strengthen the team, otherwise what's the point of the draft).