Then they can deal with those "non mainstream" sites next or adapt their regulation? I don't understand the criticism of "they can just do <x>" because it's true for nearly any regulation or law.
Using non mainstream sites instead seems like a realistic way people are going to skirt this law, and those are very hard to regulate without other unpleasant side effects on Internet freedom. I think it's a reasonable concern to raise.
Imposing a burden on a handful of mainstream websites that already invest significantly into "safety" will push people into sites that are less able or willing to do so. Unlike the target of most other regulations or laws, it is trivial to find and browse new websites and there is (almost) no cost or risk. The only way it can be effectively regulated is with draconian measures.