I think another good reason to place the glass over the liner is that most linen liners have a fairly shallow rabbet.
Adding glass, an adequate spacer, the art plus mount, backer, etc, can be difficult to fit inside a liner rabbet without having to add extra material or use other methods to keep the entire package in place.
Putting the glass between the two frames solves this possible issue.
This is an old technique.
I've had several older(maybe antique) frames glazed this way come in to my shop. Mostly people changing the frame.
One down side is that it can be hard to replace broken glass in this method.
Or to clean the inner surface of the glass.
Most of the frames I've had to deal with made this way, the two frames are nailed together, one was glued.
Very difficult to separate/pry apart without damaging one or both frames.
Using screws to attach the frames will make it easy to deal with this method in the future if needed.