The whole idea is completely barking.
For a start - under EU competition rules invitations to tender for this new boat would have to be advertised EU wide.
So you could have German /Italian / Spanish etc etc shipyard winning the bid.
Imagine the Sun headline if non-British yard was to build new Royal Yacht.
It would need a crew. It would have to be an RN crew. The RNYs was disbanded so it would need to be reformed uner an Admiral as before.
Imagine the Sun headline - armed forces being made redundant but money can be found for Royal Yacht manning
There are only 13 major warships within the RN. This new Royal Yacht would need an escort (or two) in these days of terrorism - especially if they take it through Suez and into the Arabian Sea or Indian Ocean (piracy). So that reduces the maritime capability by at least one major vessel.
They'd probably try to say it could be a hospital ship - but HMRY Britannia always managed to dodge that role.
Plus the maintenance costs, plus the fuel costs.....
There is no way that this could be done without spending any public money.
Plus the Queen would probably have given up all foreign travel due to advancing years long before it was launched.
A new Royal Yacht for Charles and Camilla to enjoy - or Charles undeserving brothers - I don't think public opinion would bear that.
Gove is just a thick psychophant who opens his mouth and spouts crap - like most politicians.