So there should be little need for mandatory boxes.
Using the GDPR to go after one big player that seriously screwed up is one thing. I certainly wouldn't be comfortable if I held Facebook stock right now.
But going after all the big players, just for not complying with something that is probably impractical for any of them to comply with, is something else entirely. How long do you think public sentiment is going to support government regulators and the GDPR if the likes of Facebook, Google Mail, WhatsApp, Instagram and SnapChat all go dark across the EU for an hour, or a day, or a week?
There's nothing unreasonable about it, it's the plain reading of Article 7 (2).
Regarding the big sites, I don't see how is that relevant to your initial point about whether "every site" will have mandatory checkboxes, and so I'll let someone else read the magic 8 ball.
Article 4.11: ”'consent' of the data subject means any freely given, specific, informed and unambiguous indication of the data subject's wishes by which he or she, by a statement or by a clear affirmative action, signifies agreement to the processing of personal data relating to him or her”