Why does ClO₄⁻ only have 3 double bonds?
I think the best argument comes from resonance.

Drawing perchlorate with three $\ce{Cl-O}$ double bonds and the negative charge on the oxygen allows for three resonance structures to be drawn (four total). This resonance stabilization  dominates the Lewis structure over simply drawing four double bonds to chlorine.

In other words, energetic benefit of charge spread out over four oxygens > charge localized on one chlorine.