That’s why spears, not swords, were the weapon of choice in war for centuries.

A 'normal' spear 6-8 feet long can offer maybe a single additional line of assistance in combat, but only at the expense of reducing the maneuverability of the front line (by the previous line needing to 'crowd' them to strike the enemy). Even in the extremely tightly-packed and not-very-manueverable Greek phalanx, which is not really typical of spear-dominated warfare throughout most of history, and reliant on intense drilling, only two ranks could engage at a time.

Ease of use, reach in formation combat, and cheapness of manufacture are the bigger contributors. Even four feet of striking distance (making some allowance for the grip position with one hand) is longer than most swords, putting an enemy at a disadvantage in that they need to approach closer than you need to in order to get a good hit in.

The pikes depicted in that drawing are typical of Macedonian phalanxes, which were revolutionary and steamrolled most the known world inside of 100 years because of how fantastic it was to suddenly be able to employ 3-5 ranks of troops per file engaged, both because of the style of fighting (holding the sarissa with two hands, even tighter formation, reduced importance of the shield) and the length of the sarissa itself (typically 2-3 times longer than a 'normal' dory spear).

To a certain extent, they were dead weight that the army carried, although sometimes they could also make a decisive contribution in a battle by causing chaos at the right place at the right time.

I would argue against this - the individual 'noble' duelists of this sort often had outsized effect on the battle, not just sometimes, but as a matter of course before strong traditions of formation combat developed. In most battles, most troops on both sides will not cause even a single casualty, at least not until one side or the other routs. The performance of such champions and skirmishers is not only severe on morale, but also in terms of materially reducing the enemy's ability to resist - in battles where one side or the other manages to withdraw in orderly fashion, you often see extremely low casualty rates even on the losing side, to the tune of 1%-2% of irrecoverables. In systems of warfare reliant on champions and 'heroic' skirmishers over intensely-drilled or motivated meat-grinder clashes, the vast majority of those casualties would be the result of those champions clashing, eliminating each other, or picking off enemy draff whose primary motivation is to cluster together, provide a screen for the champions, and hopefully not get killed.

On the other hand, the fact that a well-drilled formation is all-but-immune to such champions on foot (as no amount of skill or equipment will save you from being mobbed to death by basically-armed troops who outnumber you, locally, 5-1 or more and are aggressive enough to use that numerical advantage) means that such systems tend to fade away as states and organized military systems become more established.

Everything else you said I agree with, especially the comparison of police v. protesters. Especially relevant in tribal warfare wherein captures and ransoms remain important - I've seen that very police-protesters comparison before in discussions of tribal captures in the heat of battle, where small groups or 'champions' nab an enemy who gets too bold or too close and squirrel them away behind the shield wall.