Re barbarians > others.
Maybe in some ways but it depends on how you define "beating the game".
All the builds I have seen / tried so far have had problems. There are some ubers they cannot do without a respec - or by dying many times. There are parts of the levelling process that are difficult or worse. There are areas they cannot farm.
Is that how it is supposed to be?
When I start a character I play it with a view to how this would play in hardcore. In d2 hardcore there were always some builds that could survive all areas - and yes there were some problems such as melee builds could not survive in Chaos Sanctuary due to Iron Maiden curse (which they eventually removed) but you could build to survive )or work in a team and do well).
Although the end game is really good in Median, I worry about the fact that there is no build that can do it all in a sensible way in hardcore.
Even aerial's barbarian had places where the strategy involved dying over and over again. Totemancer is also quite good but also has a number of no-go areas. I would like to see the game design think about how to make it possible for at least some builds to do all of the game content. I realise that will not be easy.
I played hardcore almost exclusively in d2/LoD and I enjoyed it more. But in Median it would be suicide.
Other area I miss: PvP