Vault – https://getvau.lt/ – is basically the same idea, taken much further: it lets you control the character classes used in the generated password, and the command-line version can save per-site settings if you choose.
I second this. I have used this solution since I first saw it and it works perfect. The source is open so I can host my own version and it is all done in javascript. I think this is the most secure way do to this.