I don't normally comment on articles unless I've read them in their entirety, and this was no exception. I've re-read that paragraph in context several times, and I don't think it's entirely clear that you only meant it can't be done browser-side. That paragraph reads to me like you're saying bcrypt can't be used at all.

I don't think using bcrypt for this is feasible in any case. From a UI perspective bcrypt hurts you in the first place, because your feedback is going to take at least a few hundred milliseconds, so you lose the instant feedback that makes this potentially.

From the perspective of the person hosting whatever service is using this there are problems too. The first step from your "How It Works" section is this:

    On the server side, it first hashes entered password
    the same way it's done when doing regular authentication.

I'd say this is likely to increase the amount of time you spend hashing by about an order of magnitude. When you're using bcrypt, which takes a lot of computational power, I think that's likely to be significant. Especially because, in this case, you really can't afford to be queuing up requests--if you don't have the computational power to process them immediately, you get even worse at giving instant feedback. And again, that defeats the purpose of having this as a UI feature.

You having 10 years of applied cryptography experience means very little to me. Cryptography is one of those things it's very easy to get wrong even with experience. And getting it wrong has potentially very dangerous consequences.