So, the interesting thing is, there's really ZERO need to make things like reading and math "mandatory"--because of the way our society operates.
Functional happy adults use reading (and to a lesser extent, math) in the course of their daily lives, and so children who are being raised around adulds in modern society see quite plainly from a very young age that reading is a key skill to learn.
We don't teach our babies to crawl or walk--they see adults moving independently and the desire to do the same builds in them naturally.
The same is true of any useful basic skill--and arguably, if it's not useful, is it really worthy of being called "basic"?
My son learned to read by poring over the manuals to an old SNES video game system. He REALLY wanted to play the games, and play them correctly, and so he asked to sound out letters and memorized sounds until he could read the video game manuals.
He was 5 at the time. However, research shows that by the time a child is 18 or 20, it doesn't actually matter much whether a child learned to read "early" or "late"--instead, the most reliable indicator of success in terms of grasp of language and comprehension has to do with how well the child ENJOYS reading, and how often he or she chooses to read for pleasure.
Schooled kids might learn the mechanics of reading, and may read at a younger age than an unschooled child....but unschooled children are much more likely to read for pleasure.
For example, my 10 year old didn't start reading until she was 8, but she's currently on her 5th re-read of the entire Harry Potter series, and has remarkable attention to detail and awareness of the more subtle aspects of the storyline.
So to answer your question simply, no, they don't "have to" learn reading or arithmetic.
But--it's absurd to think since they don't "have to", that they won't.
Schooled kids are great about learning how to exert the least amount of effort in order to get the maximum return...in other words, getting a passing grade or getting an A.
Unschooled kids are never introuduced to the idea of learning as something to "be done with", and so they approach things that interest them in a completely different way. The learning isn't a means to an end, it's just life--and fun.
Certainly an interesting approach. Although, I do know there are some skills, which require physical dexterity which must be afforded children if there is any hope of them being competent at it. How important that is to you, is there for subjective analysis. I can't at present, make an objective case against you, otherwise.