Regardless, the model here relies on communal ownership of property. It's fine to do a mathematical proof and say that "X system is better", but something that never changes is that communal ownership of property ends up in disrepair, assuming it even gets built to begin with.
If you want examples of this, look at how former capitalist regions ended up after the takeover of the Iron Curtain. Urban decay doesn't even begin to describe it. And then look what happened to it after the fall of the Iron Curtain -- night and day difference. Another example that persists to this day is Indian reservation in the US. Nobody can actually own any property there, not even the natives. This is why it's so common to see trailers and no land improvement whatsoever. Think about it: Why would you invest time, money, and other resources to improve the property you live on if somebody can just move you out of it at the drop of a hat?
Likewise, they talk as if communism would increase the GDP, but we've only ever seen the opposite happen. As soon as you have a communist revolution (which always ends up being violent, by the way, contrast to conversions away from communism more often being peaceful than not, which alone should tell you a lot about it) you start with a GDP no worse or better than capitalism, but soon people stop giving a shit about putting work and effort into something that, at the end of the day, gives them nothing to show for it, and your GDP turns to shit. It has happened with every commune that ever existed, from the Icarians (read about them if you haven't, and how the commune ended is very telling) to the Russians. In the end, the only people who benefit and have something to show for it are the political leadership.
In fact that reminds me of this one episode of Ren and Stimpy:
In communism, the people are expected to be like how Stimpy ended up, striving for nothing more than the happiness of their fellow man at their own expense. And you know what? Fuck that. I don't care what the mathematical proof says, I'm not doing that shit.