I think if it were mythic, legendary, and cost to activate, Black Lotus wouldn't be as broken.

Rarity doesn't change brokenness, and what effect would legendary possibly have at deterring this?

You could make it cost an additional "discard your hand" and it's still broken.

Rarity only helps 'fix' a broken card if the card is excessively strong in limited formats and has proven to be a pain in the ass.
Can't tell if you knew this already or not Mystic, but... You're right: Lion's Eye Diamond

Legendary doesn't matter for BL, as you really only need one to get three turns ahead, and then it costs 0 so you could just hold onto the second one until the first one's gone. Problem with it costing anything less than to activate is you're effectively jumping ahead turns, which is brutal if you're playing a combo deck. Even at to activate it's basically Lotus Petal, which is all over Legacy in combo decks.

In short, nothing about BL isn't broken. Amazing that the guy with a PHD in combinatorial mathematics didn't get the basic ideas of tempo and card advantage (I'm looking at you, Ancestral Recall).

The postmortem we have is that Prophet Ricky and his Inner Circle knew that such cards were broken, but they decided to go forward with them anyway because they didn't imagine their game would ever grow to attract anything more than a niche following, and that among that following it certainly wouldn't be important enough to merit spending more than about 5000 Galactic Credits on, so that a player's collection of powerful cards was ultimately supposed to be limited by a sense of apathy toward the game, and different play groups would be able to experience vastly different power levels (because back then they certainly didn't produce full spoiler lists either).

Needless to say, people realized the full potential of a pocket supernova was enough to drive its own sense of value, and North Korea wanted one too, and from there it clearly couldn't be restrained.

Like.

Also, I'm not convinced that Lion's Eye Diamond is broken. It's just a good combo piece. People are more amazed that it works than anything else, but it only gets you there if your deck is degenerate to begin with (No, Thank You Yawgmoth's Will).

Sure, Pocket Supernova is broken, but it isn't the worst designed card among Ricky's Inner Circle. They just didn't understand relevant power levels when first toying with the laws of the universe. Miniature Ice Planet however was brutal and unfun. Who wants to play a game in which you could only ready one planet per turn? And that game would become miserable if your opponent had a Icy Manipulator at his disposal.

Was Pocket Supernova