In my opinion governments should require that their sites are passing the HTML Validator and CSS validator tests.
Genuine questions: Who do you think that would help, and why?
This kind of validation can be useful if you need to follow a standard for something to work. If browsers all followed proper de jure standards then this would offer a useful benefit for compatibility, particularly forward compatibility with future browsers.
Unfortunately, most of the major browsers today do not do this at all consistently. Even some of the people writing the standards have basically given up. (HTML5 "living standard"? Seriously? If it changes arbitrarily then it's not a standard.)
The de facto standards that actually matter are how real browsers behave, which dictate whether your page looks right in the browsers your visitors are using today. Nothing else you do today is guaranteed to work tomorrow without regular attention anyway, which is foolish regression from the situation a few years ago for which we can thank Google and Mozilla, but it's the reality all the same.
In my entire career doing Web work -- which is measured in decades -- I'm not sure I have ever seen an example where a project was objectively better off because it routinely enforced having valid mark-up and stylesheets. I have, however, seen plenty of cases where someone has deliberately deviated from W3C standards for a specific, useful reason.
For example, Google have been known to omit mark-up that they were sure wasn't necessary in any browser in order to save a few bytes. Multiply those bytes by a bazillion visitors to their site every day and that's a lot of traffic saved overall. Another common case is trendy MVC frameworks like Angular, which often use non-standard attributes on HTML elements for their own purposes. They could use standard "data-*" attributes, but once you've got a few of those sitting on many elements in your mark-up, it's just noise and excess weight, so they use their own prefix for namespacing instead. And yet, I don't see anyone claiming that either Google's search engine or Angular as a JS framework have failed as a result of these heinous crimes...