The european parliament can vote the bill down. But that's the last line of defense. The danger is that a lot of politicians will think that it's for the benefit of children (which is nonsense) and will therefore vote in favor of the law.

Right now it is actually the council of the EU that is preventing the law from progressing.

The "nearly powerless" refers to blocking the bill being the only thing the parliament is able to do. The commission can just keep proposing this bill, it only needs to pass the parliament once. Once passed, future parliaments are unable to amend or repeal the bill. The commission only has to win once, while the parliament has to block the bill every single time.