Yeah, heh, I don't want to be 'dude, you should retile that wall and probably the whole bathroom' but looking at that tile wall... the combination of cracked grout and smeared silicone... ick. But I have a fair amount of experience with tile and don't want to assume, heh. The wonderful thing with tile is it really isn't very expensive, it's just work.

Well, if you can get into the wall from the far side you can replace and replumb the faucet valve without demoing the tile wall and make sure that the valve is properly secured. Also, depending on if you have an accessible crawlspace and how ambitious you are you could address any water pressure issues or realize any dreams you have for an elaborate multi head shower setup by running additional lines or larger lines.

Also with the faucet and tub spout pulled you can use a grout knife to cut out all that shitty grout and sealant and regrout the wall. I'd strongly recommend using a knife and not an oscillating multi-tool with a diamond grit head unless your hands are way steadier than mine, heh. But a multi-tool would be great for cutting in from the back side. I'd also strongly recommend renting or buying a PEX-A expansion tool and using PEX-A for any plumbing as it's just an amazing system and running PEX-A into the crawlspace to sharkbite connectors to the copper lines unless you want to sweat PEX-A adapters to the copper. This allows access to the sharkbites in the future.

I know this is a lot all at once but the work is not terribly complicated, personally I think the hardest bit would be blending the drywall patch over the far side which may be harder or easier depending on how the wall is.

You've gotten good input but I will ask, do you have access to the back side of the shower wall and do you plan on living there for a while? I ask because, and please don't take this the wrong way, that looks pretty old and busted and it would be a shame if you invest time and money into a temporary fix of something you want to use for any length of time. Based on the tilework and state of the faucet it looks like it's been DIY-ed at least once already so you may want to contemplate more of a replacement and tile refresh than a patch job.