The basic answer is that energy champions work best when energy gates the usage of their basic abilities but their ultimates are only cooldown based. In the past, Kennen's ultimate used to have an energy cost, and there was testing done on putting an energy cost on Akali's ult (it didn't ever go to live or PBE). In both cases, it was found to be an unreasonable problem for the champion.
Taking Kennen as an example (his ult is majorly impactful in a teamfight). The main effect of this was that it A. majorly impacted his ability to use their basic abilities in any fight where he would need their ultimate and B. removed his ability to use their ultimate reactively if he used other skills first. The basic tradeoff was that you could either use your basic abilities and not have the ultimate available, or use the ultimate and be unable to use any basic abilities for an extended part of the fight. It was just way to gating. Energy is meant to be a limitation on your ability to fight for extended periods and a requirement that you use the energy recovery mechanics, not just a complete inability to use your full kit in a fight.
Think about other teamfight changing ults, like Sejuani's, Amumu's, MF's, etc. Unless they have burned a lot of mana prior to a teamfight, they can use all their abilities and not worry about being unable to cast their ultimates when they need to, or about being dead in the water after they ult. If Lee's ult or Kennen's ult or Shen's ult had a cost, they would be majorly limited by that. It's just not great design for energy champions.