The old picking system was not bad, but a lot worse for pubs than the current one. Cheese heros had a much higher win rate, cause you could actually get "a free game " if you saw all the other teams heroes.
Don't give me the counter picking argument, let's not forget most of the player base is low MMR, people aren't tryhards, with blind picks people can play what they want with out being pressured by others to pick that to counter X hero. Sure, sometimes you get unlucky, but it's much better than either being pressured to counter pick or just lose cause the other team counter picked all your lanes.
I don't deny that drafting is an important aspect of the game, but not having blind picks, narrows the pool of playable heroes by a certain degree. If you want for picking to be crucial, just search for ways to play CM(either inhouse or 5 man party).
As for supports picking, let's face it, they will be always first in pubs. I think more than 50% of the player base don't enjoy playing support properly. No matter the drafting type and picking order, pubs will have support heroes picked first in most of the games.
Tl;Dr This picking format is more enjoyable for pubs, cause it keeps the hero pool wider, than the previous one.
Source: https://www.reddit.com/r/DotA2/comments/qvi422/please_dont_change_the_picking_phase_cause_a/