Unless you're exaggerating to make a point, you should qualify your challenge to indicate that you're talking about old-school "brain wallets" that nobody uses anymore. Every modern wallet app uses BIP32/BIP44/BIP39 standards that guarantee a minimum of 128 bits of good entropy.
Yes, people will still refuse to back up their wallets by writing down the 12- or 24-word seed phrase, and others will get phished. They'll lose their funds, just as they already do with their Steam and eBay accounts. Your point is valid that Bitcoin allows a tremendous amount of control that many people will use first and foremost to shoot off their own limbs. But brain-wallet crackers are no longer a threat.
That seed phrase is the entire secret key making up a deterministic wallet (HD wallets, BIP32, are pretty much the only kind of consumer Bitcoin wallet today). If you don't write it down, and your phone dies or you lose it, then all your money is gone forever. In case that's an insufficient answer, here's the mechanism:
Bitcoin addresses are (usually) based on ECDSA public keys. When you send Bitcoin to someone, you're saying "send this to whoever can sign for the following public key [XYZ]. Signed, [ABC]." You had private key [abc] for [ABC], and you got the bitcoin you sent from someone else who said "send this to whoever can sign for the following public key [ABC]. Signed, [MNO]." ("said" means published to the global blockchain ledger.)
Back in the bad old days, the Bitcoin app would generate a new private/public key pair for every address. This meant that if you didn't back up wallet.dat frequently, you were screwed because your old backup might have only the old keys in it, not the new ones since the last backup.
The BIP32 scheme works kind of like this (simplified):
24 words -> 256-bit secret, called [defghi].
To generate a new address, take [defghi] and add a path to it, like "44/0/0/1" and then do a cryptographic hash on it, creating a new secret:
[defghi-44/0/0/1] -> [jklm]
Then [jklm] becomes one of the private keys in your wallet. Next time you need another key, use "44/0/0/2," "44/0/0/3," etc.
So what's nice about this is that the 24 words are the only thing you need to reconstruct your whole wallet. You no longer have to keep on backing up your Bitcoin wallet except for the very very very first time when you first create it.
But if you don't write down that list of words, and something happens to your phone/PC, goodbye bitcoin.
Your wallet can be reconstructed from that seed phrase. Writing it down and putting it somewhere safe is one way to back it up, securing your funds against drive failure.
Your answer to my comment also seems to forget what cold storage is. With cold storage, you can forget about zero-days and whatnot. It's the way to go for mass adoption (we just need to make it more user friendly).
Yes, people will still refuse to back up their wallets by writing down the 12- or 24-word seed phrase, and others will get phished. They'll lose their funds, just as they already do with their Steam and eBay accounts. Your point is valid that Bitcoin allows a tremendous amount of control that many people will use first and foremost to shoot off their own limbs. But brain-wallet crackers are no longer a threat.