Well, Sindria has a High Command and before the colony update also had the now unused Regional Capital condition. That kind of implies that High Commands were originally designed to be located on capital worlds. It doesn't necessarily mean that factions couldn't have more than one capital world, however, since the Sindrian Diktat is a relatively small faction. "Regional" kind of implies more than one for larger factions.
My opinion, though, would be that the player should be limited to one High Command and the rest of the colonies get Military Bases or Patrol HQs if they are short on industry slots. I think this could be possible without additional babysitting since the fleet sizes are being scaled down a bit.
Besides the connotation thing, I think a single High Command limit could be interesting from a gameplay perspective because it could then be used to cause additional problems for the player to solve that are not also tied to Military Bases or market share, etc. Invasions against the player only being a thing if the player has one is the obvious choice here - but there are lots of things that could happen to warrant needing or, conversely, holding off on building a High Command.
In other words, it is a late game structure for late game considerations in my mind. Military Base would be the "standard" colony defense industry alongside stations until then.