That's not how that works. It's just the opposite.
If someone doesn't expect to live much longer but can still provide a significant amount of value to others, their incentive to do it is that they can decide how the money gets used, i.e. they can give it to their kids or otherwise choose who gets it after they're not around to use it anymore.
Take that away and you take away their incentive to earn money they soon won't be alive to use themselves, which is a huge distortion.
Meanwhile people starting off with money allows them to use it, but that doesn't imply inefficiency. They don't lack the incentive to use it for something productive.
You can label anything "a mere change in market equilibrium", apparently even someone inheriting more money than the GDP of an average sized country ...
It does have something to do with inheritance. Inheritance directly causes wealth inequality because some people inherit money while others don't (and the amounts inherited vary widely). It's not the only mechanisms which causes wealth inequality, but it is one of them.
Capitalism is the private ownership of the means of production vs collective ownership, which is communism. Everything else is a consequence. I can think of state owned companies competing on price or privately owned companies colluding in a cartel to keep prices up or down, basically with no market, or any other combination. Even China's market way to socialism.
