I am not a lighting expert, but IMO a few well placed fixtures that complement the style of your home and furnishings are enough. The remainder of light from recessed, lamps and natural light.

For closets, some of the small flush mounts are actually less expensive than a recessed light so check it out before you decide. For small reach in closets, a strip light over the door pointed toward the back wall of the closet sometimes gives the most light.

I think the answer is it depends? Our mudroom has both decorative flushmounts and recessed lighting. All of our rooms (including mudroom and walk-in closets) except our living room have a combination of both light fixtures and recessed lights. To me, adding some light fixtures makes the room feel more cozy and less sterile, but you shouldn’t force it. A mix of both is ideal. I don’t think you need proper fixtures in a regular closet, but it is a nice feature in a walk-in closet.

I think I would need to see pictures and have more specifics to say if he was off-base or not.

We also have a lot of sconces throughout the house.

Here are pics of my husband’s closet - recessed light above his dresser, art lamp type sconces above the closet, and flush mount light fixtures in the ceiling

(Photos look kind of squashed for some reason on my phone)