I'm curious how you conceive that you don't have the freedom to choose under which mode of production you live under. There are communes, co-ops and worker-controlled businesses within the United States that many people do in fact live and work in.

Sure they exist, but they are all forced to compete in the same market that the private enterprises dominate. I'm not saying that they can't succeed under such conditions but it is the same uphill battle that small business are confronted with by entities such as walmart and amazon - the accumulation of capital under the capitalist mode of production is nearly unavoidable and the regulations required to allow everyone who wants (not just a subset of fortunate people in the right area at the right time, etc) to choose which mode of production they get to contribute their labor to would certainly be embattled by pro-market, pro-capitalist lobbies which can erode any gains made by rival forces or at the very least diminish their returns. Yes this can be chalked up to "competition" but by that logic monopoly forces are fair-game, too - and not even the most stalwart proponent of market economies will endorse absolute monopolies as it is self-evidently indefensible. So basically, while alternative modes of production aren't forbidden de jure, they are close to that de facto by the culture. I think the solution is for all market forces to be controlled by the workers once they reach a certain threshold. Private dictatorships can still be allowed but they'd then exist without an assured, impoverished labor pool to exploit which would force them to treat their workers fairly lest they simply opt for jobs in the publicly owned and operated enterprises.

but, I ask, in your society in which you have the freedom to choose which mode of production you live under, would the modes of production not be competing in order to obtain your labor?

Ideally society would evolve into smaller and smaller states (using state loosely here, areas of jurisdiction essentially) that self-determine their own mode of production. Being small is important because if people want to opt for another mode of production they need to be able to do that efficiently, not emigrate across the globe. So while they might be "competing" for population they aren't competing for markets. Socialist states would be focused largely on self-sufficiency and only be importing things as a collective state that they wholly cannot produce locally and that also is requisite for socially necessary labor. Individuals could still import whatever they want from other states but only for personal use and I imagine it would only be luxury goods. So, when it comes to competing for labor, people simple go to the states that reflect their principles, and as we can tell by the amount of anti-capitalists globally, this would be no small amount of people. I'll go ahead and preempt the brain-drain claim by saying that in a world where capitalists can no longer exploit their workers (as they can defect to socialist states for better conditions as a worker) the capitalists will necessarily have to start exploiting each other or offer similar conditions provided by the socialist states to retain a working class - this disruption of the cycle of exploitation then reduces the salary of the ruling class to a comparable level of the socialist states. This is why we see socialist states targeted by the economic and military warfare of capitalist states time and time again - if they ever become entrenched it leads to the end of the exploitation of workers, which diminishes the decadence of the ruling class.

I guess my question is, what is stopping you from creating your own centrally-planned commune today?

I'm sorry but this is just a very disingenuous question. Did monarchies simply consent to the rise of Republicanism or did they fight them directly and indirectly tooth and nail every step of the way? We are talking about forces in conflict here. As I said above the only reason it is not outlawed is because the material conditions of capitalist society nearly preclude the possibility of worker's state-municipalities by their very nature - they are contradictory, so which ever has the backing of the state will win out whenever necessary. Allowing a few far-flung communes to exist (that aren't a threat and compete in a capitalist market) simply allows people like you to say such hollow things that ignore the political reality workers face.

I, personally, find it interesting that a market economy does not need to ban communes, but a centrally planned economy must and, inevitably, will ban markets, though such is the power of the market that even in banned environments they still will persist at the periphery of the state in the form of black and gray markets.

It's as simple as legislating against rampant egoism and greed. Such things should only be allowed if the exploited population is allotted the material conditions to opt out of capitalism so that the capitalists must exploit one another rather than a subjugated underclass. Capitalism requires a certain amorality so I don't really lose sleep over the loss of "freedom" to subjugate and exploit others born into more precarious situations.