It seems like any sufficiently advanced business is indistinguishable from government.

In particular, a sufficiently advanced business looks like an undemocratic, authoritarian, central-planning government. Basically, the problem with large corporations is that they are communist dictatorships.

And here I thought that once you include boards and shareholders, you get something isomorphic to democracy :).

If we're considering corporations to be "undemocratic, authoritarian, central-planning (...) communist dictatorships" inside, then so are all democratic governments. The "voice of the people" part of a democratic government is just a surface layer, the tip of an iceberg. Or, more charitably, a rudder of a ship - the part that sets the course, but is nevertheless insignificant in mass compared to the rest of the ship.

The bulk of every government is a top-down hierarchical structure, because it can't really be any other way. You can't hold votes on whether a particular clerk is supposed to be in a particular building on Monday 09:00, and whether they're supposed to approve the form you're trying to submit.

That would be an oligarchy, good sir.

In a representative democracy you get a voice on who executes the orders regardless of whether you are rich or poor or smart or stupid or went to business school with who-knows-who.

Are they? Corporate shareholders have power of on-demand accountability and enough competency to grasp the goings on of a board meeting, that is not what a random _demos_ in a representative democracy is composed of and it changes the whole game, that's not a minor detail. Even besides the competency/knowledge problem, American citizens cannot, amongst themselves, zero external mediation, vote an elected official out of office as far as I'm aware.

If we were in Plato's perfect Republic where all the uninitiated adults were purged from the polis and there were only citizens trained since childhood to seriously consider matters of state, now we'd be in the same sport, if not ballpark.

That's true, and IMO, it's pretty much entirely the function of size. Modern governments are what you get when you try to organize millions of people - so it's not really surprising that, as a company grows, it starts to look like a government from the inside. It couldn't be any other way.

I'd put money on Amazon having sufficient power to control a number of desperate state governments at the least