Yes, an <?xml-stylesheet href="..."?> directive is valid in every XML document. You can use CSS to get
many of the benefits of XSLT here, but it doesn't let you map RSS @link attributes to HTML a/@href attributes, and CSS isn't designed for interactivity. That's a rather significant gap in functionality.
It is rather terrible to have two different pages, because that requires either server or toolchain support, and complicates testing. The XSLT approach was tried, tested, and KISS – provided you didn't have any insecure/secure context mismatches, or CORS issues, which would stop the XSL stylesheet from loading. (But that's less likely to spontaneously go wrong than an update to a PHP extension breaking your script.)