SSLStrip does not work on valid HTTPS requests. If you request an HTTPS page, it can not be subverted into HTTP. If it could, HTTPS would be pointless. So, yes, HSTS is not required for a valid HTTPS request. This is not some semantic argument, or some sort of side channel attack crap. HSTS is not necessary for HTTPS requests, period.
It's necessary for HTTP requests. Are you being deliberately obtuse?
It doesn't work if the user hasn't visited the site before because the HSTS header can be stripped just as easily.