The same drivers exist for Torch style landings, freeing up SLOC through the Med is such a massive saving in shipping that it's worth invading just for that reason.
For the British, sure. For the Americans - what are they shipping that needs an SLOC through the Med? The war in North Africa is over, the 8th Army is sitting around in garrisons waiting to be redeployed. Burma/Malaya/East Indies are a British problem, for the other half of the Pacific, the supplies go West from California. And even from the British PoV, the Cape route is much less of an issue if you're going to Australia, Java or even Rangoon than it is if you're going to Alexandria or Bombay.
And taking French North Africa
doesn't open the Med. To open the Med you need to clear the Straight of Sicily, which means neutralising the Axis air & sea bases in Sicily. If all you hold is FNA, you're setting yourself up for a
Pedestal-scale fight every time you try to put a convoy through the Straights and regular transport without major fleet support is impossible. And to neutralise Sicily is extremely difficult (BoB flashbacks) without occupying the place, which means a major invasion and a land campaign. Are the US really going to commit to a major campaign against the French, so they can launch a major campaign against the Italians, just so the British can get to India faster?
Carrying out any other landings in the Med without clearing your supply lines from your home ports is idiotic just down to the extra shipping needed to support any invasion having to go round the Cape will be difficult to find while supporting the war in the far East and building up forces in the UK.
True, but is that an argument for taking FNA/Sicily or for winding down operations in the Med? Churchill no doubt will be filled with ideas about the Balkans and the "soft underbelly"; the US may be less keen.
It would be faster and safer to bring oil through a pacified Med from the middle east to build up stocks in the UK for any invasion onto continental Europe.
The largest source of oil and especially refined fuels is the US - any stocks in the UK will mostly come from there.
Logistics dictate that Algeria and Morocco must be brought under Allied control one way or another.
Why? The Allies would be happy to sail convoys along the coast of a neutral Morocco/Algeria. If the Luftwaffe or RM were using bases there it would be different, but currently they aren't. The logistical roadblock is further east and the big problem is Sicily.
They need to control at least one side of the Strait of Sicily, but it doesn't have to be the African side.
The problem is that they need the Axis not to control either side, and getting to Sicily is a problem if they don't hold Tunisia.
OTL, before invading Sicily, the Allies had control of Tunisia, a large and somewhat battle-hardened army already in Tunisia and indications that Italian support for the Axis was wavering. TTL, at the current time, none of these apply.
There's also the possibility of taking Sardinia.
Sure, but why? It has no major port, poor infrastructure, it's on the road to nowhere and getting there requires a voyage of hundreds of miles through waters subject to enemy airpower. Grabbing islands for the sake of grabbing islands was what led to the OTL fiasco in the Dodecanese.