I use a similar tool (pwdhash) and the benefit is not that it's a single password but a single root password. I need only a few changes and very little to remember for most sites and still get a unique password per site.

My bank requires me to change the password every 3 months or so and I only need to change on digit in what I remember and they see a whole new password.

It's a great benefit to me and to overall security.

How secure is it overall? Somewhat more secure than just using a single password for all sites and better trust compared to using a cloud based password storage.

You don't have to memorize them, though. If your master key is "bananas" and it didn't work, try "bananas2", "bananas3", etc. But you don't need to remember them all—because they're all essentially the same.

Hopefully this happens infrequently enough that it's a non-issue anyway.