The interior doors in most houses that I have seen have wooden frames in which it is very easy to make holes for passing cables. Some newer houses might have door frames made of plastic or metal, instead of wood, but even in such cases it is much easier to make a clean hole through the door frame, instead of through a wall.
I have made many such holes in door frames for passing Ethernet cables or TV coaxial cables.
When you do not want to touch the walls, such cables can be routed on the edges between walls and floor and they can be masked by a cover having the wall color, to be invisible, except where passing through a door frame.
Why would you prefer to make a hole in your doorframe rather than the wall? Sheetrock is so much easier to deal with. But perhaps you are referring to a concrete construction, which is uncommon in the US.
Making a clean hole through a door frame takes a few minutes at most, with an electric drill machine, after which you pass the cable through the hole, you crimp the connector on the end of the cable and you are done.
At least in Europe where I live, I have not seen any walls through which you can make clean holes with high probability. Almost always there is some small damage, which must be repaired, e.g. by filling with plaster and/or repainting. In most cases you also need a percussion drill machine, not just a simple drill machine. Here most walls are made either of concrete or of bricks.
So at least in the kinds of walls that I have seen, passing a cable through a wall requires more time, more diverse skills and a larger set of tools and materials than passing a cable through a door frame, which requires only that you have and know how to handle a drill machine and a cable crimping tool.
While common outside the US, most of it in newer constructions tends to be light concrete which is trivial to drill. But even 40MPa concrete is fine with an SDS, rent one if you don't wish to spend money on. In short drilling through outer walls is not difficult either.
I have made many such holes in door frames for passing Ethernet cables or TV coaxial cables.
When you do not want to touch the walls, such cables can be routed on the edges between walls and floor and they can be masked by a cover having the wall color, to be invisible, except where passing through a door frame.