The core difference, of course, being that there's an in-built mechanism for meritocratic selection and failure. Big companies that "centrally plan" first of all only get there by establishing merit via product/market fit (unlike dictatorships), and if they fail, they usually go out of business or fade into obscurity (unlike dictatorships). If Sears was anointed the supply chain central planner on account of its one-time dominance, there's no guarantee that they'd "thrive" forever.

One might then decide, okay, it's really dictatorships that are bad, let's add democracy on top of the central planning. Except...there's no empirical evidence that democracies organically elect central planners that yield the same kinds of outcomes as the "big companies". In practice, democratically elected planners have been selected more on the basis of their political clout, rather than on the basis of their merit. An example: Tesla is arguably the foremost "central planner" in electric cars today[1]. And yet, the White House recently snubbed Tesla in a summit on the future of electric vehicles[2]. California's state government not only drove Tesla out, they've decided to allocate EV resources towards laggards like Hyundai[3]. The political calculus is obvious: Elon Musk is politically unpopular among the base of voters that anointed the aforementioned democratically elected governments. Nevertheless, it's quite the indictment of democratic planning. Another observation: if the United States decided to centrally plan supply chains in 1997, there's no way they would have selected Jeff Bezos to be the politically appointed commissar[4], despite him (and his company) probably fitting your description of a "big company in effect that's a large centrally planned economy that's thriving". The opposite is happening, where factions of the currently elected government are determined to relieve Amazon of its role as a "central planner", despite (to your admission) its effectiveness.

At least with dictatorial planning you might (if you’re lucky) have a competent dictator/bureaucracy that might have some unified plan / vision with the leeway to install politically unpopular but highly competent planners (and therefore no accountability), and you can actually get some stuff done. You see this with China and Singapore, which are both more authoritarian than liberal democracies (especially China), but generally have fast moving development — though even they rely predominately on the private sector / markets for their growth/development. With democratic planning/resource allocation, nothing ever gets done because at best it’s basically design by committee, and at worst it's a popularity contest where the most competent "planners" lose if they're simply unlikable.

Also, there's really no big company on the planet that's centrally planning every single price signal in an economy — not even Amazon. They're dominant, yes, but by no means are they the sole producer/distributor/allocator of all goods and services. The largest corporations account for single digit percentage of GDP (if even). This is not true of state-driven central planning, at least historically speaking.

The nuanced reality is that, yes, at some layer, we're all central planners. The family unit is usually centrally planned, and so too are corporations. The empirical lesson we've learned (historically) is that once you get to a certain size, there are diminishing returns to effectiveness of central planning, and at worst after a certain point it becomes actively detrimental to the well-being of the economy.

[1] https://www.nytimes.com/2020/07/22/business/tesla-electric-c...

[2] https://www.theverge.com/2021/9/28/22699339/elon-musk-joe-bi...

[3] https://twitter.com/DavidSacks/status/1393342790931664899

[4] https://twitter.com/JimPethokoukis/status/123124591376463872...