Casters (long rest types) only dominater in single encounter adventuring days. Martials dominates in longer ones.
I think that's a somewhat misleading claim.
Casters benefit most when they're in a situation where they can basically drop one of their higher-end spells every round. Single encounters days certainly allow that, but in fact I don't think they'll show peak dominance, because at levels above about five, that's likely to be underkill - i.e. the caster will have quite a few strong spells left.
Given most encounters, last, what, three-four rounds (last I heard), a 5th-level caster can potentially drop a 2 3rd and 1 or 2 2nd level spells in that period (which might be upcasted versions of lower-level spells). So he does perhaps favour one encounter/day or at most two to really be superior.
But by the time you get to 9th-level, it's looking more like three encounters/day is pretty favourable to casters, and I'd suggest that broadly this trend continues, at least up to a point.
So rather than claiming that one encounter/day is the
only situation casters dominate in (which is the stated position), maybe note that the longer the day, the more likely Martials are to end up in first an equitable position, and then an advantageous one, and that at higher levels, the number of encounters this takes increases. Pretty sure 6-8 was chosen because of this. As an aside, personally I still think it's excessive - characters of all classes should progress so it's more like 3-5/day is ideal imho, but that would take an entire new edition to do, so is irrelevant to this discussion.