The minimum amount required to stake is 32 ETH. That’s $75k at today’s price. There are cheaper was to “stake” but those are not really “ETH PoS” staking. So no, it does not “cost less to stake”.
My claim was that the lower ongoing expense of staking is compensated by lower rewards, so that both systems have similar profit for similar capital outlay. In setups where mining expense is almost zero, the higher rewards of mining give it much more seignorage than proof of stake.