Game systems are not demonstrative of how tags should work in general: their usage is exceptional and breaks the rules of how tags get used, but we do it that way because it works really, really well without causing any trouble. Every other tag is demonstrative of how tags should work: we tag based on information already in the question.
Describing the content of the question is how tags work by default. From our help center on tags:
A tag is a word or phrase that describes the topic of the question.
When the text of a question seems to carry no indication of why a tag is there, the tag does not belong and gets removed and never added. Tags exclusively describe the content already there, and do not add new information themselves. A question about casting a fireball doesn't get (or keep) the armor tag unless it's clearly a question that is also about armor, for example.
That's the default, at least.
Game system tags are a useful exception
Some stacks have tags that are an exception to that rule. On RPG.SE it's the system tag: we don't need you to say "I'm playing D&D 3.5e" somewhere in every question if the question is tagged dnd-3.5e. This is like how on Stack Overflow nobody asks you to tell them the programming language you're using as long as your question is given a programming language tag such as python or c++.
This is an exception to the norm. It's an exception we've developed because it causes no trouble and is pretty intuitive. So you're right, we don't treat them the same way. But this doesn't mean we can start using other tags the same way without causing trouble.
We did treat RAW that way for a while, and we specifically stopped because it was causing trouble. I'll get to that in moment.
And in fact, even if the body makes it clear which system it is using, if the Q is not yet tagged with the specific system (not the same as using the system-agnostic tag), we wait until the querent tags it with a specific game system first before answering.
That's not quite how it is. When it's clear what system they're using, we just add the tag and move on. However there's only one circumstance we count as being clear: they say explicitly what system they're using in the question text. In all other cases, we don't
guess, and we do what you're describing there.
Rules as Written is not (any longer) an exception
Until 2016, we handled Rules as Written like system tags: if you add the rules-as-written tag to something then suddenly, regardless of what's in the question text, it's now a rules-as-written question and only rules-as-written answers count. This was a problem because a lot of people didn't understand what using rules-as-written meant, and thought it was equivalent to rules.
The community collectively endorsed a change to that plan in February 2016: A low-intervention approach [rules-as-written]: back to tagging basics. As the name suggests, we've gone back to the basic tagging practices I described at the top for how the rules-as-written tag gets used: the question gets the tag if it's clear the tag belongs, otherwise, it does not get the tag. If it has the tag despite it not belonging we ask for clarification on why they added it, and then modify the question to clarify why the RAW tag belongs or to remove the RAW tag because it doesn't.
There aren't other exceptions
We judge the content of your question and what tags it should have by what's written in the title and body. It gets tags that correspond to that content, and tags never add new information that wasn't already there. The sole exception is the system tag which is allowed to clarify the game being used all on its own.
Your question is only a statistics question as long as it would be read that way going solely by the question's title and body. Then we add or remove the tag based on whether it is truly a statistics question. Adding the statistics tag does not, itself, make an otherwise not-statistics question a statistics question.