If they made energy champions costless like Katarina, Zed would be completely broken. I can't say much for the other energy users as I don't play them as much. Zed is slightly limited right now because of his energy costs but if you took that out, he'd be able to play unrestricted. Zed with 40% CDR at max level has some pretty low cooldowns:
- Q - 3.6(s)
- W - 8.4(s) and lasts for 5(s)
- E - 1.8(s).
Once Zed reached the cap, he could throw 2 shurikens and spin 3 times, everytime, all while his shadow is on an 8.4 second cooldown. This would mean that he would be able to throw a shadow down, spam Q and E, wait 3 seconds, and do it all over again. His W shadow stays in place for 5 seconds and the cooldown starts the moment the W is thrown. Zed could literally zone everyone out just because he can spam abilities over and over even while far away.
Normally, with energy, this wouldn't be possible unless Zed managed to hit every single ability prior so that he could have barely enough energy. He wouldn't be able to do this again until his energy bar was completely full. If this happened, I can tell you with 100% certainty that every Zed player would play way more aggressively (and likely win more trades) because now, for one, they don't have to watch their energy bar and two, unrestricted costs would make him be able to deal maximum damage every single time, not just when he lands all of his Qs and Es. Did you honestly think this was a good idea?