In most cases you can still make a viable deck, but everyone will have to deal with largely mediocre cards they wouldn't have picked given the chance. Granted the system isn't perfect, but it seems to effectively level the playing field and encourage creative deck-building. Not sure if Hearthstone has an equivalent mode.
It's also interesting to me that the "meta" in Hearthstone not only can, but does change regularly, when people discover deck archetypes that beat the currently dominant ones. Especially when deck types that fell out of favor at some point show up again later because the decks that countered them too hard also fell out of favor (I think variants of Freeze Mage has done this twice?).
This kind of evolution of the meta happens in lots of games, but of course notably in the ones where players themselves refer explicitly to a meta amongst themselves and keep track of it.
Thats why I think co-op games end up being far more satisfying, since they don't have to balance out a player vs player arms race.