If the minefields work and contraband cargo is shifted to other ports out of reach of the Houthis transportation net then the missile attacks should diminish. Once their homegrown supply begins to dwindle they will (have been) become selective of targets. A launch pattern can then be determined and a second flight of F-35B aloft ready to perform a ground strike.
Having many warships is great but we get back to the problem of supporting them far from friendly and capable ports. Minefields negate the need for many warships. An LHD can supply LCS with fuel, food and weapons while staying out of reach of Houthis missiles itself. If an LCS should breakdown or get itself sunk a Burke could come up as replacement. Its economy of force while taxing the economy of force of the Houthis. You have them now reacting to Allied moves.
Defensive missile fired off from Burkes is great but only solves one aspect of the problem. Ground attack performed by the F-35B and minefields solves two more aspects of the problem. Offensive air support is what is truly needed in this situation not defensive missiles, that is if you wish to solve the problem and not prolong it.
You can substitute Burkes for LCS if you wish but if the F-35Bs and minefields effectively do their job then one does not have to worry about reloads of the Burkes’ VLS.
The LCS are not equipped to defend merchant ships against attacks with ballistic missiles, anti-ship missiles and drones. They only have a RAM or SeaRAM launcher and could maybe defend themselves.
A pair of Burkes is not sufficient - that is the problem. There are more warships present, but the area threatened by Huthi attacks is simply very large and then the at least four warships currently present are not sufficient.
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