Brawl, above all else, is a format about expressing yourself through specific colors and working within the natural confines of those colors to achieve victory in your commander's own style.

So when your Azusa opponent hard-counters your commander with Counterspell and reclaims it with their green cards, or your Thassa opponent casts Day of Judgment, what on Earth is even happening anymore. This isn't Magic. With no color pie or expressive color identity, this is just YuGiOh. Key to the Archive functionally and objectively breaks the spirit and balance of the color pie, Magic's linchpin game mechanic.

Also consider the card's general strength. It effortlessly slots into literally every Brawl deck that curves out higher than 3 and provides the opponent with a miserable situation. It must be immediately destroyed to deny the opponent the pie-breaking color fixing, and even if they can AND do it, most decks can still find ways to cast the spells through mana rocks, treasure, and ilk. It's an unbearable two-for-one that also gives the opponent a Demonic Tutor for their mono-white deck or Counterspell in mono-green.

The card also fuels degenerate five-color good-stuff decks like The First Sliver. If it isn't destroyed, you untap with two extra mana and the game is probably over at that point. If it IS destroyed, you still just get to cast the card. And nothing feels worse than destroying Key to the Archive because you can't afford your opponent ramping, only for them to untap and cast Demonic Tutor. It's easy to say with certainty that Key to the Archive becomes a stronger card with more colors in the deck, and that's the last thing Brawl needs for balance.

The final reason to ban Key to the Archive relates to it being an Alchemy card: Alchemy cards do things that are impossible in the paper game, so cards printed for the paper game have no chance of interacting with them or effectively countering what they can do. Alchemy cards completely shatter game-states and are miserably overpowered because most of them, in one way or another, create a two-for-one interaction. They either draw cards, create treasure, seek spells, or just conjure free cards altogether. You will never encounter an Alchemy card and be able to cleanly deal with it outside of using counterspells.

Key to the Archive is a feel-bad, broken, ubiquitous mess of a card. It is a pandemic in Brawl and should be banned outright.