Capitalism is a system for society that rewards ownership of goods and territory. It is an effective system, partly because it plays to natural human instincts for ownership and control of one's environment.
However there is a definite difference between ownership and attainment, and attainment benefits an individual better than ownership. That which benefits an individual benefits society because a society is a collective of individuals.
Ownership requires no action and in can encourage laziness. Those who do little work but make a living from ownership are the sort people that early and contemporary socialists object to. Nobody objects to those who work and are rewarded for it.
The word fair has been omitted because it is not helpful. Like "better" it is a meaningless word mainly used by politicians, and normally used in an almost antagonistic way. Just as better infers that the present is inferior, fair infers that the present is unfair. Everyone desires fairness and something better. The only way to obtain the better is through attainment not ownership. Fairness, however, can never be attained except in the spiritual mind. Fairness is a human emotional concept. Existence is either fundamentally unfair or fundamentally fair depending on viewpoint; either way fairness levels cannot be altered!
In essence a modern capitalist society already rewards attainment as well as ownership. Attainment also plays to natural human instincts and the differences between "attainmentism" and capitalism are relatively small.
Income tax and V.A.T. or sales tax are taxes on attainment. Taxes on bank savings, on property (council tax), inheritance taxes are taxes on ownership. A more attainmentist society would tax income and sales of goods less, and tax ownership more. Acts such as gaining bank interest that result in gain without energy should be restricted.