It did for me. The "This is a list of blogs and news sources I follow." part of the page as rendered comes from the XSL file (opml.xsl). The actual list is rendered. I'm did not check whether the XSL was applied correctly, but applied it was.
> On Firefox, ["view source"] showed be the XML file.
Can confirm.
> The idea of downloading XSL, [...], I find that idea compelling.
> [...] but when I found out the browsers weren't really playing along anymore, kind of took the wind out of its sails.
Sad, yes, but for me Firefox did download the XML, the XSL, applied the XSL, and rendered the resulting page. I dunno why it didn't for you or GP, but maybe it's an add-on interfering? Do check, and please report, because I'm curious if the issue is add-ons.
edit: and yes opened the link on a new tab
It opened fine in Safari (macOS), and it opened fine in Chrome. Firefox did not apply the XSL file.
I tried to "view source" on both Safari and Chrome, and neither gave me the option. I could Inspect Element, and I got the HTML DOM, but not the original XML source. On Firefox, it showed me the XML file.
This surprised me. I was under the understanding that the browsers had effectively abandoned the XML/XSL concept any more. Apparently Firefox does.
It's also a shame the browsers stopped at XSL v1 as well, v2 is much better.
But, the browsers basically said "we're not in the XML ecosystem, we're in the HTML ecosystem".
The idea of downloading XSL, and then having a blog post that was little more than just content, with a wee bit of meta data, with all the chrome rendered locally via the template, I find that idea compelling. One less thing to download. More stuff to cache on the local system.
I had grand visions of an XProc pipeline terminated in the browser itself, but when I found out the browsers weren't really playing along anymore, kind of took the wind out of its sails.