Prove email and phone are required in online services

I'll pay you $160 if you can prove mathematically that the only way to offer online services without spam is by requiring people to provide an email address or a phone number. That would be an interesting result.

If this can't be proven mathematically and you are an online service then please answer: why must online services require users to provide an email address or a phone number to get service? Why is no other option offered to the user?

Why is it impossible for a human to use online services while not having an email or a phone?