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.

I was thinking something similar to Rafi89's reply just a bit ago:
If you can get to the plumbing from the other side of the wall, it could be what you need to do. Go to Youtube and look up Vancouver Carpenter on how to cut, and then patch a hole in drywall. He's got lots of great drywall vids. Once you've learned a little about how to do it RIGHT, it isn't so hard. But it's easy to do bad drywall jobs. I was doing bad ones for years until I found his vids.

Maybe you DON'T have to do this, and you can find cartridges that will replace what you've got. If you don't see the right thing at Home Depot or Lowes, find a plumbing supply, and pay a little premium for the free advice they've given to help you find - or not find a replacement.

However, I also do NOT like the looks of that grout. I suspect if you took some of that tile off you'd find black mold from moisture underneath. If you started taking tile off, you'd quite possibly end up putting up complete new concrete board to replace the sheetrock and doing new tiling. I wish you luck, and hope that regrouting does what you need!