Oh yes it is extremely hard working off your kitchen table. The plans of my first home in the post shows how small we had to work with. I was working off the kitchen table.
The Home we are building has a study down stairs which is large enough for a library. Instead of a theatre room we will have a sitting room. This will help when we have visitors and meetings. I didn't want a theatre I thought they were pointless. However they do have insulated walls so maybe might have been good to do that.
Upstairs will also have a lounge and a corner study in it. Only small and in our main bedroom there is a walk in robe which is quite large and I can set up an office in there. I'm thinking I will need a separate location as the kids get older or for my wife away from everyone.
The world is changing and it will be a more at home version of it.
Perhaps you could have a concealed motorized projector screen so you could convert your library/sitting room into a Theatre with comfy sofas that could be used for entertaining and lounging? Just a thought since you already have insulated walls. Yes, it's always good to have your own private office set up separate from the kids whenever possible.