Power grabs doesn't require financial system to be happen. Even in a non existence monetary system country, power grabs can be happened.
What would be the point?
If Humans have access to all necessities of life and most (if not all) wants on-demand... what is the point of 'power grabbing'?
The reason that power grabbing happens today is because we live in a socio-economic system that actively promotes such a way of thinking in the first place and creates a setting where it is actually possible.
'Grandiose desires' of domination, etc. stem from a distorted value-system and society that promotes such behavior.
A technologically developed society such as ours without money would realistically do away with governments and people in positions of power because of automation (even governments are delegating decision making to machines to a large degree already - or basically, you arrive at decisions by relying on the information that is accessible via technology) and exposure of the population to relevant general education.
There is simply no point to having a government if an entire population is exposed to relevant general education, because, the more you know, you are less prone to being manipulated/used, are capable of governing yourself, and can even think in a critical capacity along with being a problem solver (industrial education as we have it now does NOT expose you to generalized information in all fields that is actually IMPORTANT, nor does it prompt people to think critically or be problem solvers).
Politicians and bureaucrats are useless - they are NOT problem-solvers.
They don't create change - they mostly serve to perpetuate the status quo and keep things as they are.
They 'might' make some token changes in an existing system, but that is nothing more than 'patching' or 'treating the symptoms', whereas the underlying cause is never addressed, hence we end up with even bigger or that much more problems down the road.
All of the lazy people died in the aftermath of WWIII (you don't work, you don't eat - there's no welfare in the apocalypse!), so there were no lazy genes to pass down.
Genes are responsible for physical traits.
Behavior is environmental - starting from the early stages while we develop in the womb.
And while Humans might be born with certain 'tendencies', whether or not those tendencies manifest depends on the environment you grow up in, along with information/knowledge you are exposed to.