Doubtful, and a difficult policy since most ships are dual fuel so what governs? Going to pure LNG is not likely a cost decision that one would pursue solely on the basis of mooring fees.
And what incentive would there be for the port? Why would they lower their fees for LNG? They’d be providing the same services at presumably same costs so they’d have to increase non LNG fuel fees to cover a discount and that risks driving away ships. Actually, if they begin allowing LNG bunkering, the port would incur new costs, since the port would have new issues to deal with that require specialized planning, training and risk management over traditional fuel.
Small, localized, incentives like mooring fees are not likely to drive behaviors in any meaningful way. The shift to using LNG fuel is being driven by macro level approaches and international emission targets more than this could produce. The technology has to be available to be selected and in trying to change an industry’s traditional energy model it only develops in broad target based schemes such as the emissions regulations implemented by phases for ships leading to increased use of LNG seen ongoing now. It has to be a force large enough to create a market for the tech.