I used to view capitalism as an inherent part of the society we currently live in, with no real economic competition.

I think it's best to approach this by asking what capitalism is. I see it as a distributed computing resource allocation system.

That is:

1. Decision-making is decentralized. Each agent has private information and communicates with the market through 'prices.'

2. Actual decision-making / computing is going on; agents are choosing between alternatives, constructing portfolios, gathering information, and so on.

3. There are some scarce resources that could be used to satisfy multiple different desires, but there's not enough to satisfy all desires.

You can construct an alternative by flipping those descriptions. For example, rather than a decentralized system, you could have a centralized system. This is empirically worse off, because we don't have easily scalable centralized computing, and information transfer is hard. (If you've already got billions of biological computers running around, why not make use of them?)

A zero marginal cost society is one in which we can satisfy all desires, without ever having to face tradeoffs between those desires. While this could eventually be possible, it seems unlikely, and is more likely to be accomplished through editing our desires than editing our environment. What's more likely is that the sort of things that we consider costly will change.

For example, consider a moon colony where air has to be filtered, to process CO2 back into breathable O2. You either have a bottle exchange, pipe connection to a filtration facility, or pay for the cubic and wattage to have plants that do your filtration for you, but 'breathable air' is a thing you budget for and part of your utility costs. On Earth, breathable O2 is zero marginal cost, because there's so much of it lying around.

Water is only slightly more expensive--yes, bottled water isn't cheap, but tap water is two and a half gallons for a cent. (People in the US use about 80 gallons of water a day, or about 32 cents a day, but rare is the person who drinks over a gallon a day.) So water is 'minimal marginal cost'--people will typically turn a tap on without a second thought if they want some water, but people also only consume ~4 times their volume in water a day, rather than hundreds or millions of time their volume.

Food is again more expensive, but still cheap enough that it is rare (in the developed world) to not have enough to eat, and cheap enough for government programs to fund distribution programs with only mild taxation. Most don't think of food as being zero marginal cost; it's typically expensive enough to get mindshare along with the rest of the budget.

But suppose that everything physical becomes as cheap as water. You decide you want a cup of Earl Grey tea, hot, and so you 'turn on the tap' and there it is. You decide you want a motorcycle, and so you 'turn on the tap', and there it is. At that point, what is the scarce commodity that is wanted more than had?

Some obvious things come to mind: status, attention, time, and so on. Bits of information are already cheap enough to transfer that many websites generate elaborate content to attract eyeballs, because sometimes those eyeballs click on ads or buy t-shirts or donate money. We already live in a world where people make professional salaries by designing clothing for electronic avatars. Even in the world where everything physical is free, it seems that there will be things for 'capitalism' to operate on. (You can imagine the differences between a capitalist attention economy and a communist attention economy, for example.)

It seems unlikely to me that we will reach a point where the physical world is as cheap as water in the next several decades--I think that 3D printing will be roughly competitive with current manufacturing (factories can make a lot of things very cheaply, and precision 3D printing may be finicky enough to require factory-like conditions), and we already know that renewables aren't as cheap as non-renewable energy (that's why we're going to all the trouble of drilling that oil). If energy isn't zero marginal cost today, more of it coming from solar isn't going to make the costs any lower!