We have billions of literally biological brains making many economic choices every day. Our current economy is a very distributed organic engine, it wouldn't work unless everyone contributed by deciding what to buy with their money.

It has central parts but the main decider in the engine is what consumers choose to buy.

Which is influenced by what products consumers can buy in the first place and what products they know and have a good impression of - which is in turn influenced by the decision of large distributors and media companies etc...

This even before getting into financing and regulations.

This assumes that people have access to accurate, up to date and unbiased information to make informed choices about what to buy.

Yes they buy things, to what extent the things available/popular are the product of a free market vs established conglomerates having regulators in their pocket for example is highly debatable imo.

How many of these giants would survive without a steady stream of government contracts?

This is a great discussion. We should define what the engine is.

United States spends ~3% of the GDP in defense. Obviously this creates markets but there is a relatively centralized decision to spend that amount of money.

There's a book "The People's Republic of Walmart" that makes these arguments. Walmart is a massive company, as large as some entire countries even, that operates an internal economy based on central planning. They tell all their suppliers exactly what will be produced, in what quantities, when it will be delivered and largely what it will cost. Modern stock control systems and supplier integration make it feasible.

Calling walmart centrally planned is a massive mistake. Walmart is only responding to what its customers want. That is not central planning as it has ever been used to describe an economy. Central planners repeatedly tried to dictate what consumers want. Walmart is quite literally a market, the opposite of centrally planned.

Responding to purchasing decision by downstream consumers is what the USSR tried to. In theory you would buy things, the price would be slightly higher than the cost, and whatever was being bought more would be produced more, with the profit reinvested in trying to make new products and services. In practice organizing the production efficiently was too difficult due to a confluence of a dozen factors.

Point being, responding to consumer demand is indeed what central planning is supposed to do.

And in practice, every level that has a say in the central planning - even at Walmart - tries to impose other agendas. What they would like to see more produced and consumed as opposed to what the would be purchaser wants. In Russia it might have been that someone wanted to drain off some money, while they knew some regional admin who wanted their figures to look good, etc up the chain. Result: garbage tractors and not enough of them. In the US, with central planning, gas engines are penalized or electrical ones are pushed - whether you think this is a good reason or not.

At least in the US, if Walmart central planning insists on procuring crappy paper towels, there is a good chance that their competitor Target, literally across the street, is at least ignoring them and perhaps even deliberately exploiting their mistake.

Free economy doesn't mean that a business shouldn't try and plan the hell out of things. It means that each business planning process is not the only one around, and all these business are free to have various obsessions (ethical, religious, racist or whatever - none of them traps everyone in), and all these are free to have other blind spots and bugs, etc. They do have bugs. They look for each other's bugs and respond to them.