There are many criticisms of this economy that we currently have, and the creeping monetization of the last vestige of private life in which we don't need to currently sell, those hours after work and before sleep.
"Why exclude this?", as you ask, simply shows you think that there is no space to resist the totality (I would sometimes go as far as to say tolatitarianism) of "the economy". No space is free, because we have given up resisting it.
All economies are made of people, some of whom do not make resource allocation decisions (because they are unable to or prohibited). I see no reason to start talking in terms of the population of an economy rather than other factors first. Marx, for instance, used property and classes, because he noticed that individuals are born into pre-existing situations, as defined by the class and property structures of the day, and they do not shape the world freely as they see fit. It takes effort to individuate.
> including no system at all (which would just be the ultimate free market)
The "ultimate free market" very clearly has a "system" - it has private property rights, separation of the labourer from the product she makes during the production process, the majority of labour being waged labour, and the general economic goal of capital accumulation. If the free market really meant "no system", but still a reality, then we would have observed it in the most basic societies. Anthropologists have found no evidence of that claim.
>which is just a system where resource allocation decision making is taken away from individuals, and placed in the hands of a central authority
No political philosopher uses this definition; most forms of socialism (theoretically, anyway) are democratic, in which allocation decision making is given to the people, to a higher degree than it is in a capitalist society. Finally, in such a system, individuals have the greatest degree of control over capital, not just labour allocation (through which capital is influenced only directly).
>and decision to allocate a finite resource is an economic decision, including decisions to devote time, effort or attention to something
It is not purely an economic decision, it is also a moral and practical one. Only the economist, strangely, conceives any and all time as a pure "resource" to be allocated around. The view that activity is equal to allocation of finite resources ignores the reasons why people actually perform various activities. Sure, you could subsume every motivation into allocation of finite resources, but the physicist could go further and subsume every interaction into the interactions between atoms. Why should I (or anyone) prefer your level of abstraction rather than saying it is too restricted (e.g. as the physicist would say) or saying it is too wide (e.g. as the sociologist would say)?
>Wanting topic of passion to be excluded from this system defies the laws of nature itself.
Marx noted in the 19th century that economists, like the priests, have a preference for speaking of their ideological view as "natural law", that previous systems were "unnatural", that future possible systems are "unnatural". He realized that this tactic ensures that nobody can question the foundation of the concepts (atomistic individualism, Hobbesian warfare, resource allocation, the origin of money, capital, power, property) since that would be to question "nature" itself.
>just completely defies any sense of reason.
It defies purely economic reason. Today we see many people and hobbyists taking such an "unreasonable" stance, from charity and open source workers to musicians. People, as it turns out, are not rational economic actors (the "resaon" you speak of is a prescriptivism from neoclassical economics), nor do they judge their time as a resource ("time is money" is a mantra that only seems to apply during the business day). There is no evidence that counting time primarity as an economic resource was prevalent in previous societies.
On that note, unless you're monetizing the time you spend posting on HN, you are completely defying any sense of reason. Either that, or you can tell me about your spreadsheet of resource allocation for your day down to the hour by the time you next make a comment, and the calculated opportunity costs associated with each hour.
Economies are made of economic actors, which includes ALL people as well as other entities like public institutions, companies, charities...
> some of whom do not make resource allocation decisions (because they are unable to or prohibited)
Every single person in the world is an economic actor. Every single person in the world has the ability to make resource allocation decisions, even if they are only using the labor of their own mind. The incarcerated are economic actors, even literal slaves would still be economic actors.
> most forms of socialism (theoretically, anyway) are democratic, in which allocation decision making is given to the people
A theoretical “democratic socialist” country (theoretical because people have voted socialism in, but never in history have they been allowed the privilege of voting it out) would be a country where the people surrender their natural rights to make their own resource allocation decisions (or at least a significant portion of those rights) to the government.
> The "ultimate free market" very clearly has a "system"
It doesn’t at all. It’s just the way humans (and really all animals) behave in absence of governance that prevents them from doing so. Ancient people most certainly had private property, even if it was shared within the tribe or family or whatever other format of social organisation. It would also pay for you to remember that Marx thought familiar or tribal affiliation was a source of evil, as families tend to care for each other, which he considered to be terribly unfair to anybody who didn’t have a family to care for them.
I would very highly recommend that you at least learn some basic economic concepts (what an economy actually is would be a good starting point) before you go around promoting the abolition of private property.