No. You should not be able to earn coins without contributing to he network. In pow, miners earn fees and block rewards. In POS, staking nodes earn fees and % of their coin. Rewarding a wallet for existing is pointless. If everyone has 1% more coin tomorrow, no one is better off than they were today.
Well not everyone will be staking. But through staking, you will be in essence freezing the supply of tokens. If demand remains constant, then it increases the equilibrium price, that would actually make everyone better off. Especially those staking and receiving rewards for it. Once more people catch on to this idea, we'll definitely see more POS coins doing this.