Since you didn't specify what kind of test are you talking about, i'm discussing this in general terms.
Many of this so called "validation test" are just a syntax check with a DOM of reference, this means that an high score is for a well formatted source, a lower score is for documents that does not respect the DOM guideline.
The main problem with the HTML is the fact that is an interpreted language and you do not have an implementation of reference and also the values and the attributes that you can use within the language can't be associated with an unique behaviour or an unique result.
Most of the times you also end up with the need for some hacks that can break your syntax check, sometimes is better having an uncorrected syntax rather than having an HTML page that looks ugly and can be rendered in the wrong way.
From what i know i also can't define Usability/Accessibility because this 2 words can have an infinite numbers of definitions, for a mobile user this can mean a website with bigger buttons, for a person with some eye problems can be interpreted as a better color contrast in the page; this really depends on what are you targeting.
As I said, this tests are just a syntax check but their real meaning is around zero or less, some clients can require thos little logos at the bottom of the page but i do not think that they know what a webpage is made of and how it works.