Yes. That's a feature. You can log on any computer, and access your coins, with no server and no state.
But note that "if 2 people have the same password" means you can guess someone's password. And not being able to guess passwords is an assumption that any and all password-based systems have to make.
Avoiding guessable passwords is easy: implement verification of the password strength.
>And not being able to guess passwords is an assumption that any and all password-based systems have to make
The difference being that you're not testing against everyone's password at the same time. Also using an extremely strong password means a large number of people are going to forget and thus completely lose access to their wallet. I'm not sure this is a solution to the problem of barrier to entry to bitcoin.
I disagree about an inability to remember/store a password, creating a "large" barrier to entry.
There exists many ways to securely store passwords. For one, educate users that it is OK to write down the password offline as long as it is stored securely in a safe, or in your wallet, which you already trust for your cash and important documents.
But note that "if 2 people have the same password" means you can guess someone's password. And not being able to guess passwords is an assumption that any and all password-based systems have to make.
Avoiding guessable passwords is easy: implement verification of the password strength.