The "rules" need to move with the times,
And of course that's exactly how they got there in the first place. Go back to the 1930s and there were lots of pilots offering flights in aeroplanes. At some point there were accidents and government ruled that they had a responsibility to ensure that fare paying passengers were as as safe as possible. From there the AOC was borne. Private pilots were not regulated in the same way and therefore the standard of safety is unknown. For that reason they were not allowed to carry fare paying passengers any more.
The reason why advertising in a flying club is permitted is because those who frequent flying clubs are likely to be aware of the lower level of safety regulation they enjoy. Frankly, the Internet has little relevance, clubs could have a website and if that's how they communicate with members then I doubt that any court would rule that unreasonable. The spirit of the rule is that you don't advertise in the public domain.
If you want to go back to every pilot offering flights for cash, then it will not be very long before someone has an accident and the public will demand yet more regulation, quite probably making things more restrictive than they are now.
It seems that the only people who really push this issue are those who can't afford to pay for their own flying, or those who want to bolster their own ego by impressing unknown people with their unknown skills. Thank goodness we have an aviation regulator to protect the public from such people.