Although it is a truism to state (without evidence) that people are inherently selfish and greedy, I doubt that this is actually the fact.
There may be plenty of evidence that where relations are organised by an economic system (eg reward based) predicated on expansion of market and exploitation (of people and the wider environment) that leads to increased inequality and therefore problems of social order, it is necessary to have checks and balances to keep the cycle going. But this is because of system dynamic not human nature. Also the checks and balances are campaigned and fought for rather than charitably given - eg 'gender' pay gap, minimum wage etc.
But selfishness and greed do not determine non economic relations where labour is freely given - family, friends, community. Do you invoice for everything you do? Do you consider yourself to be selfish and greedy? Is your giving inherently selfish? Do you give without expecting reward? Do you think carers are angels or stupid because carers allowance is a pittance and those cared for are rarely grateful?
Wider than that, people freely give their time and labour and 'intellectual and experiential' labour to help others for no monetary gain on this board (see SEN threads, relationships etc - maybe not AIBU!). See also the socialisation of capital needed to fund health, education, pensions etc. See also how new technologies release beta versions to be improved, peer to peer collaboration etc.
The truth is, capitalism could never and cannot continue to exist without free labour. Often provided by women. Perhaps this is the kernel developed under capitalist exchange that will enable a better way of doing things?