Or is there anything special about read-write, such as both being on paper, as opposed to listening and speaking, that makes it worth keeping?
"Read-write" sounds a bit awkward. I would prefer "written-language" (or "written"). I hope we don't get an overly jargony word like "orthography".
There may be questions (such as this one) which warrant both tags. Many questions will be only about one of these two.
Merging these two tags (reading and writing) into one, is harmful, as it doesn't allow us to tag questions which are specifically about reading or writing, and not the other. Having three tags (reading, writing, and reading+writing) just pollutes the tag echo system, and makes questions harder to find.
There may also be a case for a writing-system, which is distinct from the skills of reading and writing.
Likewise, speaking and listening comprehension are distinct skill sets, and ought to be tagged separately.
As the author of the single question with that tag, I feel compel to explain my rationale.
Reading and Writing are separate skills. However, you can hardly read if something isn't written. Or write something you can't read.
Let us consider two examples:
For European, to learn Chinese or Japanese, they could stick to pinyin and romaji respectively. That way, they will learn to speak, oral communication, etc. Or they can learn the ideograms, and then learn at once to read and write in complement of the oral communication.
For young children, they learn to communicate orally from the beginning. And typically from ages 4-7 they learn to write and read, usually in parallel.
So while they are two different skills, in many learning process, they are combined and separate from speech.* This is the reason why I combined them in a tag. And I would not oppose changing the tag to the two separate one, but I think it does not make much sense.
*: note that Speech Learning comprise of Speaking and Hearing. Are we going to separate those as well?