A paused game is not like a paused video where there is no processing going on. A paused game still has all the rendering usually going on (unless the developers got time to implement something custom), audio still needs to continue, the only thing actually paused in the game logic and gameplay elements.

Given this the game needs to slow down and lock its frame rate while paused and in menus otherwise it will run at full speed and burn a lot of CPU & GPU time. Though I would say this is not usually an issue because it gets fixed pretty quickly during development.

Now more work can be done by the developers to make the paused state this efficient, but it is all a matter of priorities, and in all cases the developers would rather spend their time making the gameplay better and fixing crash bugs. If the player wants their game to run more efficiently then they should reduce the processing demands by limiting the frame rate and lowering quality settings.