My take on this is the old unions aren't decrepit just because they're unions and they've existed for 100 years. I don't think it's built in to the nature of unions to eventually become decrepit (no more than any other institution anyway).
Their problem is not that they're old, it's that they're not powerful enough anymore to be the kind of adversarial force they once were. They're shrinking instead of growing. Their strategy, if they even have any, is built around defensive self-preservation and survival. It's a siege mentality.
There's a reason for it, and a history to it. In the first half of the 20th century, upstart unions were on the rise, growing all the time, taking over everything, expanding into new sectors, gaining power. There really was a time when it was reasonable to think eventually just about every job in the country would be union, and that's just how things are. Perfectly normal. (And generally speaking, those young unions were more spontaneous and democratic than their progeny today. They were more "bottom up", less bureaucratic. Also much fightier.)
But capital isn't stupid or defenseless and they fought back. The result, for a while, was the Fordist paradigm that ruled the postwar years. The idea was union leaders and management leaders could work together and reach compromises that were acceptable to both sides, and overall productivity and quality of life would be optimized through this kind of give-and-take. We're all Americans, right? We all have the same goals (even if I own the factory and you work in it).
Well, that's all gone now. From the 70s on, the formerly powerful unions got totally pulverized. One major weakness they had is their own leadership had, in the compromise period, gotten pretty cozy with management and formed a kind of "labor aristocracy" whose interests were more aligned with management than the rank and file. This is basically the state the old unions are in today.
In other words, the developments were contingent on dynamics of 20th century history, not the only thing that could have happened. The problem with 20th century unions is not that they have some innate structural flaw, but that they lost the fight.
I don't think we need to re-invent the concept. The boss owns everything you need to do your job, and you have to have a job. You lack power and control over your working conditions. As an individual you can't do anything about it. Banded together with the rest of the workforce, you can. This is a concept everyone can relate to already and I don't see any utility in renaming it for the new generation or something.
I used to drive a 30 year old beat up car. One day somebody crashed into it and smashed it up. I tried fixing up everything I possibly could, but eventually I realized the engine was completely shot, the block had been cracked, and the thing just wasn't coming back. I didn't rebrand and go get a hoverboat or something. I just got another car that wasn't wrecked.