It is a rather transparent combination of
reicht so // as is, like that
reicht auch // too, also
reicht schon // yet, already, well
PS: indeed, as another answer says, auch is not strictly needed. However auch schon is an idiomatic collocation. If some kid says "Das habe ich schon", the eager friend will respond "Ich auch schon"; Or maybe ich auch, which would appear like an ellipsis (nevermind the lack of an inflected verb in either case).
But the so is more interesting, as Latin se, "without" compares well. Therefore, "Spass hast du so schon, deshalb brauchst du keine Rollschuhe" may have a very different meaning than the other so's; There are so many of them, so that I have to reason further like so: A relation to sole "alone, without" is obvious, and a relation to in this one way and no other is thinkable.
The importance of auch in this collocation, might be the contrast, "you won't get it this way and not that way". Indeed, the Dutch cognate ook means "and".
It would be skimpy to say that auch had just creeped into this phrase by accident, that it was used in redundancy for good measure. We do call phrases fossilized, if the words are not used productively anymore (ie. what is lieren in verlieren, forelorn? Or verletzen and what does it have to do with lust?). Since many senses of auch are used productively, it would be a stretch to call this phrase a fossil, but the gist is that children simply copy the language and rationalize it as they go. What anyone thinks when they say it is of little concern so far, because there may not be one unique answer. So I hold etymology as an important part of interpretation. Although, its etymology eludes me so far. I mean it is well enough a rather volatile idiom, too, like many other conjunctions (cp. Greek O kei; Ger oder auch?).
schon appears like an amalgam of schön and En soon, maybe with a hint of shunt, i.e. "close* ... or rather meaning early, morning following a complicated argument I already forgot.