What preclude two people from choosing the exact same secret phrase when creating a wallet, other than it being highly probable? Would both parties not have control of the wallet?
This topic has been brought up many times since bitcoin first introduced this method in 2013.
In short, yes, if you chose a simple phrase and someone else did the same. You would each have control of the same set of private keys.
In reality this is highly unlikely, and the math is out there in regards to guessing a phrase.
With 10,000 computers guessing 1 billion seeds / second (not at all feasible to check balances that fast), then assuming there are 2 million funded wallets (there aren't - there are only 2 million non-zero addresses on the blockchain) then,
3.402823669×10³⁸ / 10,000 / 1x109 / 2x106 = 1.701411835×10¹⁹ seconds to find any one of those seeds. Which is about,
539514153540 years
I think we will highlight what type of phrase should be used more prominently and possibly link off to a mnemonic phrase generator