Why not?
Why not? And I like the idea, too.
You know, all the King's horses - Kings of Persia - FAILED to stop the Greek phalanxes. Among other reasons, it's because they were spear-armed. Why would it go differently now? Yeah, the spear's shorter than a pike, but if a horse tries to run down or push a phalanx, the horse's still likely going to get poked.
And, remember two more things: plenty of protesters are both experienced and sophisticated at what they do. They already often act in sync even across causes of action. High modern idle times, transportability, and communications give protestors alot of potential. Some protestors are even paid pros.
So, suppose an Athenian protest group of Marxists had formed two years ago. They decided it'd be cool to resurrect the old phalanx formation for protests, carrying their signs on their spears. A leader volunteered to organize it. A subsequent discussion decided to pad the shields and spear ends to help with legality and peaceful message. A web site published the ideas.
A core adopted it as their hobby and practiced alot, though most were alot less enthusiastic.
At the next protest they attended, taking Eurail, the core were put in the lead and other key areas. There was no clash at the first protest, and by the end of the event, they had basic discipline and movement down. 'Most everybody else was envious of them, and their site got many protestor community hits after that. Plenty of non-Marxists showed in padded shields and spears in the next event, and even eventually joined in. This time a battle happened, and the phalanxes were eventually routed after a long successful stand.
The group's leader wrote a long constructive criticism, explaining what had happened, and what should happen differently next time if they wanted to stay in the field next time. There were extra practices, and more attended.
The next time a clash happened, they stuck; and vendors were selling padded phalanx gear. Everybody kept reading the criticisms after each battle. By today, there's enough veteran core to stick in most battles.