Agh, tiers are a lie.
They are not. The unanimous consensus among all competitive players (some of which are the best players in the world) is that tiers exist. They argue that it would be almost impossible to balance a game of unlike characters; without specific redesign, characters would have the tendency to fall into tiers by dint of their myriad variables (differing attack power, running speed, etc.). Furthermore, the developers cannot foresee top-level strategies, and thus even their deliberate efforts could fail to balance the game at a professional level. Years of empirical results support this conclusion as well; national tournament-winners of Melee almost always use Marth, Fox, Falco and Sheik.
I guess among noncompetitive players, a low tier character could be used just as well as a high tier character (possibly due to the fact that the low tier user is just a better player than the high tier user), but if two master players are in a match (the highest possible metagame) and one is using Pichu and the other is using Sheik, chances are the player using Sheik will ultimately win. It's just common sense; Sheik has amazing combo capability, intense speed and several advance techniques (wavedashing, fast fall, etc.), while Pichu has poor grab and attack range. On top of that, he is easily comboed despite his light weight (not to mention Pichu inflicts self-damage). Pichu has some good points, but his cons far outweigh them while Sheik's pros outweigh her cons (and her cons aren't as crippling as Pichu's).