Oh I agree with your thoughts 100% for myself. On a personal and individual basis your approach is one that I would follow for myself personally and encourage others to do so as well. It is sound and it is holistic. Holistic is what is key.
You are correct, the boundaries are artificially subscribed. they allow us to put things into neat little boxes that perceptionally allow us to control and manage our lives.
Family, Work, Weapons, empty hand training, golf, playing with the kids....
all go into neat little boxes that we open, focus on things in what we percieve to be the most efficient manner and we close it up and move on to the next one.
"Combatives" training for military can be approached this way as well. One thing I do like about the Marine Corps program is that they at least formally recognize that the sum of the parts equal the whole.
They also have a motto "One Mind, One Weapon".
Unfortunately, most out there will use the "box" method of management of their lives and have "gaps" where the stuff that does not fit definitionally into a particular box gets lost.
These gaps prevent us from synergy and seeing a bigger picture sometimes, and can affect our development/evolvement.
Yes I do think you are correct in your approach.