I think the general expectation is that, unless the lawyers find a way to weasel out of it somehow, they will eventually make the standards available for (free) download just like the text of the directives themselves. The standardisation bodies have been complaining quite loudly about how this could destroy the whole standards system. But I think it's ultimately just about the money. A large part of the CEN/CENELEC budget already comes from the EU anyway and I guess there will be some renegotiations and then everyone will move on.
So yes, this will mean shifting some costs to taxpayers. Personally, I think this is fine. Given the fact that we essentially allow industry to write their own, legally binding, regulations through the standards system, the public should have the right to scrutinize them. As a side effect, it lowers the barriers to entry for small businesses and reduces the burden for freelancers.
My understanding is that if the court had struck down copyright on the standards as well, then someone could go and publish them all by themselves tomorrow. The court decided not to rule on that question, so everyone has to request them individually for now or wait for the Commission to figure out their new system.