Terminating Cat cable into wall sockets is straightforward. The cable will bend okay in its sheath, and you'll strip off part of that leaving a short length of the 4 twisted pairs exposed, so routing gets easier still. Coax is fine too, though having a couple of RG6 cables fighting for space inside a dry lining box can make it a bit tricky to close things up without kinking a cable or popping out a grid module socket. You can get around some of this by the routing path for the cable before it gets to the backbox, and then making some additional holes for easier cable entry into the box.
The problem you'll have is with HDMI. The signal standard can be fussy about what's in the chain from source to display. This is particularly true if you're sending 4K signals. Have a look at some of your existing HDMI leads. Those plugs are not small. The tail and strain relief adds to the overall length. You have to try to fit that inside a drylining box and get it to line up with the grid module's rear HDMI socket, all without damaging the cable because you bent it too far and now the signal doesn't work, or having the grid module pop off all the time because the pressure from the back is just too much for the little plastic tangs to hold the socket in place. Then you plug in the HDMI cable to the front face of the grid module, and the leverage plus weight of the cable makes the module fall out anyway. Argghhhh!!!
Eventually you give up and go for a single or double gang face plate with 1 or two HDMI sockets. Now though you realise that you need to cut the wall to add some more sockets for any other cable connections. Oh, and you can't return the expensive grid modules because they're used.
Okay, now you got all your cables neatly in the wall and a bunch of wall sockets which ended up being spread over two feet. That's so you avoided any timber battens and left enough plasterboard between the sockets so the wall is still strong enough to support the dry lining boxes. It's more space taken up than you really wanted, and it took a lot longer and cost far more than you originally envisaged, but it's done. Now you come to hang the TV and the next problem rears its head.
The HDMI cable sticks straight out from the socket and fouls the back of the TV. Oh crap. So you go off to the web and find a vendor of 90 degree adapters. It arrives and you go up to make the connection, only there's a problem. You connect the adapter only to find that the fly-lead now points up the wall rather than hanging down. Bugger. There are two types. You didn't know or the supplier picked the order wrong. You mess around trying to sort that.
Finally you got your connections. The wall plates aren't falling out. The cable at the wall hangs down in the right direction. You've plugged in the HDMI lead and dealt with the excess cable that was poking out just below the TV. Great. You fire up your 4K source. No signal. Eh?? You switch through the AV inputs. Still no signal. You try to see which HDMI socket it's plugged in to and check the connection at the wall socket. It all looks okay. You even go to the trouble of taking the TV off te wall, undoing the wall socket and checking that the HDMI cable is correctly inserted at the back. Then you put it all back together again. Now you're absolutely sure which HDMI socket it is on the TV, so this time you know you'll get a picture.
Still nothing. WTF?!?
Now starts the real troubleshooting, and eventually you realise that either some bit in the chain isn't as 4K as the supplier lead you to believe, or just that having so many joints in the 4K path makes a mess of things.
This is why we use brush plates for HDMI connections. One cable - point-to-point - any excess tucked away in the wall. No joints, no adapters, no problem routing the cable to fit behind that low profile TV bracket you fancied. One day, job started and finished. TV by teatime. Maybe even half a day if things go smoothly.
Been there. Done it. Bought the T-shirt.