Brainstorm is an absolutely legendary card in the overall scope of Magic: The Gathering as a game.
First printed in 1995 in Ice Age, it has been a defining feature of many now defunct formats, as well as Magic's oldest formats in Vintage and Legacy. It was so ubiquitous in Vintage that it was actually restricted, joining the likes of the Power Nine and other broken cards like Sol Ring and Channel. However, it has remained, to this day, legal in Legacy despite being one of the format's most played cards year in and year out. It has escaped the ban hammer in that format because, like Sol Ring in Commander, despite its power level it is considered a crucial part of the format's core identity. (Whether that last statement is true or not is a topic for another article.)
As such, when the Mystical Archives of Strixhaven were announced to be legal in Historic and Brainstorm was on the card list, there was some trepidation. Historic was a format without fetchlands, one of the key components of eternal formats that makes Brainstorm so good; could the format handle it? This is a very complicated question, but let's not get too far ahead of ourselves and start with the basics.
Why Is Brainstorm Even Good?
Before we get to the specifics, I want to briefly go over why Brainstorm is such a good Magic card.
A ban of a card like Brainstorm feels a lot different than a card like Oko, Thief of Crowns or Uro, Titan of Nature's Wrath; Brainstorm never directly wins you the game, nor does it interact with your opponent or their cards in any way. It doesn't provide card advantage, kill things, or answer threats, so as such it feels very innocent because all it does is use a mana to make your current and future turns much more consistent.
However, despite how hard players fight against it, inconsistency is what makes Magic, well, Magic. We build our decks to be as consistent as the game will allow, but there's still a wide variation both in our opening hands as well as our first few draw steps. We need to be able to plan for this spread, so our deck will function well when we get the upper range of our hands (a perfect curve out, timely draws) as well as adequately the lower range of our hands (missed land drops or colors, incorrect answers or threats at incorrect times).
Brainstorm takes this spread of possible outcomes and slices off the bottom part of the range, so what's left is smooth and consistent in all the ways you want it to be.
"Brainstorm decks" will never be an overtly oppressive part of the metagame unless something else is also broken in the format. In that case, Brainstorm will make those decks even better and more resistant to hate. In the case of a balanced format, Brainstorm just makes every deck it is in much more consistent, making not playing with Brainstorm feel like you are handicapping yourself. It doesn't draw ire like Eldrazi Winter or Hogaak Summer, but giving every Blue deck +5% to their win rate is a quiet, but huge, deal.
Which leads us to...
The Case For Banning Brainstorm
As we can see, banning Brainstorm is less about fixing a "broken" format and more about trying to dispel consistency and uniformity in deck-building.
Pretty much every Blue deck in Historic is playing four copies of Brainstorm, running the gamut from more aggressive decks like Izzet Phoenix, to pure control decks like Jeskai Control, to control ramp decks like Bant Control, all the way to combo decks based around Indomitable Creativity. The only Blue decks not playing Brainstorm are usually centrally focused on some other thing like creatures for Collected Company or auras for Kor Spiritdancer.
This is a large part of the reason why Ponder and Preordain are banned in Modern, while also being the reason why Brainstorm is restricted in a format as powerful as Vintage. You have cards that are so efficient and universally good, you need to find a good reason not to play them rather than a reason to play them. Basically, every Blue Legacy deck starts with 4 Brainstorm and 56 other cards, which reduces the number of playable cards in a format by a lot.
There's also the issue that Brainstorm is particularly good in both combo and control decks. In the former, it excels at finding combo pieces and shuffling away unneeded cards, while in the latter it helps to ensure the control deck has the right answers at the right time. These are often the kinds of decks that cause problems in formats, so it makes sense to deny them this tool.
Of course, this is not a clear-cut banning.
The Case For Not Banning Brainstorm
Let's make one thing abundantly clear... Having Brainstorm legal in a non-fetchland format is awesome!
One of the coolest things about Magic is how much context matters, so seeing a historical all time powerful card outside the context of playing alongside fetchlands and Magic's most broken cards is a rare and beautiful thing. When Brainstorm was announced it wasn't even clear if it was going to be good in Historic, as historically it has been underwhelming in formats without proper fetchlands or high-quality shuffle effects.
One could definitely argue that if Fabled Passage wasn't legal, Brainstorm may only be seeing serious play in Arclight Phoenix decks that really want a critical density of cantrips. It wouldn't be flexible enough for the control decks or even the combo decks unless they had additional ways to shuffle. The issue there is when the next Fabled Passage comes along, what do you do then? Brainstorm would essentially just be a ticking time bomb, just waiting for whatever cheap shuffle effect or new engine it would enable to be printed before it would finally need to go. Brainstorm is so powerful it's hard not to imagine that it would be an if, not when scenario for it leaving the format.
Another big plus for Brainstorm is how well it plays against what once was the format's best card, Thoughtseize. Thoughtseize, as well as the somewhat perplexing Mystical Archive addition Inquisition of Kozilek, is an extremely powerful one-mana play in a format that is lacking on good things to do on turn one. Like Brainstorm, Thoughtseize is a Legacy/Vintage power level card, despite being a very different kind of card. There aren't that many ways to counterplay against Thoughtseize, but Brainstorm being able to tuck cards safely on top of your library was a nice one.
There's also just the general heuristic that banning cards sucks.
It always feels bad when something is taken away from you, even if you recognize it is for the greater good. Players who have invested time and money to build a deck that utilizes Brainstorm will be losing both the monetary investment of their deck, as well as the time and emotional investment in getting good with or enjoying a deck that will no longer be a legal option. Ban fatigue is a real thing and you can only take things away from people so many times before they just give up and go do something else.
Not Banned... Suspended!
Okay okay, technically Brainstorm is not banned but suspended, which basically means they just won't give you back your wildcards for banning the card but you can't play with it. A suspended card has a chance to be reintroduced into the format, but this is an extreme rarity. Frankly, the entire notion of suspending a card feels like a racket to get people to shell out more wildcards for a new deck when their deck is banned, but hey what do I know?
To be completely honest, I'm in the middle with this ban.
Yes, Steam Vents decks have been the best thing to be doing in Historic for a while now, but this has as much to do with a suite of powerful prowess-style threats built around Faithless Looting and Arclight Phoenix, great control options like Memory Lapse and Lightning Helix, powerful combo options like Indomitable Creativity and Mizzix's Mastery, as well as the universal power level of Expressive Iteration and the other Red and Blue cards.
I don't expect these decks to drop off that hard with the removal of Brainstorm, although their general power level will definitely be going down, but if people are sick of playing spells over and over against Memory Lapse, getting attacked by Arclight Phoenix, or being comboed by Mizzix's Mastery on Magma Opus, I'm not sure that banning Brainstorm really "solves" any of those problems.
Historic probably would have hit a point where Brainstorm needed to go, I'm just not sure if that point is exactly right now. The upsides I have listed are very relevant and I'm not sure the format is better with Brainstorm gone than it is at present.
Of course, this could also just be the start of a cascade of bannings when it comes to the Mystical Archive cards, as there's a chance they came in a bit too hot. Either way, we shall see!