It's been a while, but I remember getting into an argument with somebody about this some time ago and digging a lot for red posts.
The truth is, Riot has never explicitely talked about blind pick. But the fact that they did speak about draft pick (and ranked, back then) as well as their reasoning behind endorsing pick order and the name itself ("pick order") implies it's really about the order in which people get to pick their champions, not the positioning of the portraits.
That means that in blind pick there is not actually any inherent pick order to respect.
A simple thought experiment also makes it clear that pick order can't really be followed in blind pick:
What if the topmost person doesn't pick until 5 seconds before the game starts? Do all the other players have to adjust their picks within 5 seconds to respect his first-pick status? If not: How long does first pick have time, etc.
It's a simple rule for draft pick, for blind pick it's either a extremely complicated or terribly ambiguous rule, neither of which are a good idea (or consistent with Riot's general philosophy)
tl;dr: Pick order emerges naturally and intuitively from draft pick. Blind pick is inherently chaotic and impossible to regulate as long as people get to pick at the same time.
