I think if you consistently did this you would end up overpaying, for a few reasons. It's pretty common for offers to be made on the high side as an incentive to sign on, for example. People could get higher offers from places that have less appealing work (i.e. the job is not more valuable overall). Generally if you're always matching the highest offer, you're probably paying above the fairest sustainable wage.
Being that open about it would mean employees would let it slip, and you'd be a target by competitors to raise your costs far higher than they'd need to be.
