I think you're misinterpreting the intent of what you quoted. I also think the phrasing of that definition is quite sloppy, being prone to exactly the sort of misunderstanding we see here.

For a market to be stable, fair, and free of monopolies government intervention is required. I don't think that fact is at all controversial. So already the definition you've quoted there has, if read literally, set up a scenario that is impossible to realize.

A free market is one where regulations are broad and are applied to the players evenly. A subsidy that applies to a sector as a whole (ex solar panels) is an example of such.

Many of the agricultural subsidies are much more targeted than that. However the regulator needs to maintain the stability of the entire system as a whole, and to that end food is not some luxury good that can be subject to shortages without major consequences. A tradeoff has to be made, either for more market regulation or significantly less market stability. Market participants in danger of starvation not known for exhibiting reasonable, well thought out behavior.

Similar to free speech, the free market is better seen as a vague guiding ideal rather than an absolute and objective description of a system. It's illegal in the US to make credible threats of violence towards someone. Can that fact be taken on its own to mean that we don't enjoy freedom of speech?

I am not misrepresenting the intent. The definition says “without government regulation”. If their intent was that some regulation was allowed, they would have said that. It’s the job of a dictionary author to be precise.

If I define a “two legged stool” you can’t add a third leg just because two legs is unstable and doesn’t lead to good outcomes. Whether a market with no government regulation is stable or leads to good outcomes does not change the definition.

You are referring to a “mixed economy” which has some markets and some regulations. A mixed economy is more stable because it is able to reduce market failures like monopolies and externalities that free markets cannot escape.

You're arguing semantics and have rendered the term meaningless in the process. The purpose of a dictionary is to communicate meaning. The meaning of a word or phrase is the idea that it is employed to communicate in practice.

When people talk about a free market they aren't referring to some logically contradictory thought experiment. It is something that they actually wish to strive for in practice. Thus it is clear that some amount of regulation must necessarily be involved.

This is quite similar to freedom of speech, as I previously mentioned. The concept itself is an abstract ideal and the context of the law matters.

What you are referring to is a laissez-faire market which as history has repeatedly shown doesn't remain a free one for long. An adjacent comment pointed to property rights as an example. You can have a free real estate market without having a laissez-faire approach to property rights, yet the government involvement in that case is extremely heavy handed. The free speech analogy might be a city controlled by the mob where the government won't intervene but saying certain things will still get you killed.

I agree with you that in practice the US is a mixed economy, but then I already acknowledged that (among other things) our farm subsidies are highly targeted and the medical sector is regulated in a very invasive manner. However I do not agree with your suggestion that eliminating monopolies makes a market mixed. A monopolized market is not a free one because there is no competition.