Yeah I don't believe your analogy relates to the OP which is why I jumped in. I appreciate that you're asking questions rather than most of the numpties who refuse to learn anything about our designated boogeyman.
Communism is not about distribution at all. It’s about common, collective, or social control of the means of production. The biggest difference is between capitalism and communism is that the people actually doing the work, not the capital owners, decide how to divide goods - nobody gets rich by simply owning something (like a factory owner or landlord). The economy is much more democratic and less oligarchic/authoritarian like it is now.
Hard work is actually rewarded - the more you work, the more responsibility you have, the more important skills you have the more "money/status/perks" you receive or have access to. So to put it bluntly, your pay depends on your contribution to society, and “perks” are often more important than cash payments
As I mentioned earlier, it's more about social equality - not equality of outcome but equality of opportunity. An analogy with the current system is that poor folks would have access to the same higher education that wealthy would. Talent, not money or class, determines success.
I'm a student of all types of economic systems and communism is easily the most misunderstood of all of them, simply because it is generally not taught in the US. I'm not necessarily an advocate but I do find it interesting, especially given all of the obvious challenges that our current system faces. It's incredibly hard for us to imagine because the current system is the only one we know.
I don't believe in handouts or those that don't contribute to society being rewarded, but that's precisely the system we have now. We all know somebody like this. Owning something is more rewarding than work.