Well it's obviously a better experience for someone who's not the page author if the browser tries to render an invalid page rather than throwing up its hands and showing an error. That way you can at least try to read the page rather than not being able to and having to track down the author and try to get him to fix his site. The "strict parsing" fans tried to force correctness with XHTML, but it was a failure and didn't see much use.

The main problem with "handling the slop" used to be that different browsers would render invalid HTML differently, so poorly written sites could look very different depending on the browser you used. Modern HTML standardizes how browsers handle invalid HTML so this isn't a problem anymore. See https://html.spec.whatwg.org/multipage/parsing.html