Court fees are proportional to the cause, like 10%. At least in Germany, only that has to be payed up front; Paying the lawyers comes later. So the cost should be within income,and in cases where it isn't, procedures are in place to excuse the plaintiff. Filing should be relatively straight forward, safe any catch-21s that require a lawyer, that I not being a lawyer don't know, but even a lawyer could not foresee with certainty right now.
A real problem would be the usually long wait.
However, taking into account several more circumstances, either side might not be keen on a court case, and thus provide to avoid it. That hinges on morals and technical details.
The problem with copyright's blurry edges around the originality threshold hasn't changed at least. The Olympics organisation is famous for suing, and loosing often enough, over its trademarks, for example.
> take on a major media company in court
In court or outside? And why the media companies? Laws can be repealed by supreme courts on constitutional grounds. That's an even bigger judicial hurdle to consider. If lobbying or legislative orders are involved, it would be a superset of the problem, as the court is to an extend bound by the lawgivers interpretation of the law, disregarding any side effects that are implementation specific. That's the undefined behaviour of the law. The service nulled all your bits after you passed ownership? The content wasn't registered initially and you assumed it was licensed to null? Ohohoho, none of those side-effects were mandated.