I lived at a commune for a month and you are right that no private property depresses ambition and care.
However, a wealth cap is not the same as a tax that completely levels the playing field. There is still ambition to reach the cap. People with this sort of drive, despite Ayn Rand's fiction, will not just stop playing. They can't. It really is a complusion. They will just be forced to play by different rules.
The old yacht analogy for trickle down is the way that poor people think of wealth. The utlra wealthy are not buying a million yatchs- they buy corporations and assets. They buy from each other. Instead of trickling down- mergers and aquisitions lead to massive layoffs, and bankruptcies. This leads to the loss of real assets for workers, like their house or car. The debt trickles down, not the rewards.