How problematic is the trend of young people today not identifying with a political party? Not problematic at all. If anything I see it as a major plus, assuming they are still engaging in the political process. Not being subject to a particular party and its platform basically forces you to do your own research to see who the better candidate truly is.
What would really be nice is no political parties at all. Even politicians who might be otherwise decent people have to sell out to parties to receive the support necessary to run a competitive race. In true life, candidate Doe might be anti-abortion, but if he does not vote on the pro-abortion rights party platform, no checks will be heading his way next cycle.
As for what a ‘young’ party would look like, I think you are seeing it in the Libertarian party. Young people want as few people telling them what they can and cannot do as possible, so a socially liberal, fiscally conservative party like the Libertarians seems like a good starting point.
Who knows if a third-party will ever be viable? Many have attempted and they always end up losing steam after a few election cycles. Maybe Libertarians can make it stick, maybe they cannot, but even the bit of influence they have can make a big difference in any given election. This reasoning is why there is no such thing as a ‘wasted vote,’ even if your candidate cannot win.