I fail to respect opinions which lack logic.
Yes, other vessels (not 'any' vessel - they need certain on-board facilities to do the job effectively) can do mine clearance. But do you want the supply ships which should be supporting the fleet, the amphibious ships which should be transporting troops & equipment, etc., tied up in mine clearance?
The world wars are not a good model for today. If we ever have to mobilise as in WW2, then we'll have to build a new navy, army & air force - but we're far more likely to be engaged in smaller, shorter, wars, which start with relatively little notice. Requisitioning merchant ships, fitting them out for minesweeping, & crewing them, takes time - too much time for all but a long, major, war. We need to have vessels which can do the job straight away, & won't be needed for other essential war-fighting tasks. Having a patrol fleet which can just load up the USVs, etc., take aboard the specialist crews, & go to war, gives us that. Relying on requisitioned merchant vessels doesn't. They'd take too long to be ready.
No, we don't have a frigate in the W. Indies now, but what happens to the Bay-class or whatever happens to be there at any particular time if we get involved in a shooting war somewhere? It's very likely that it would suddenly have more important work to do. And so on for other taskings. Also, we're cutting RFA numbers, along with escorts. Hence the requirement for something smaller & cheaper to buy and operate, to take over such taskings.
For the purchase price of a Typhoon you wouldn't even get a BAM. Your more heavily armed ship would cost a few Typhoons, & getting the numbers you propose would lose us a few squadrons of an already undersized & under-armed air force. Yes, you could get a few for the price of an Astute, but can we cut submarine numbers even more? The only way to get what you want is to cut something else we're already short of, or increase defence spending - and the latter won't happen.
Note that the SFPA operates unarmed vessels, with limited capabilities, & not available for deployment elsewhere.
BTW, in a short war the rule of three is temporarily suspended.
What is the point of having a warship that as soon as its anything beyond a bloke in a boat with an RPG you have to send in a real warship.
Because most of the time, in most of the world, the bloke in the boat with the RPG is the most you have to face, & having something which can deal with him effectively & at modest cost enables you to concentrate the real warships where they're needed, instead of spreading them around all the places where that RPG/boat is the greatest threat.
We currently have two escorts in the Somali anti-piracy operation. One is acting as a command ship, but a BAM or similar could replace the other, & in extremis we could replace both with such vessels.