If there is a complete frame of the 1x4s on the inside, the plywood will effectively just be cosmetic, with some reinforcement against racking. But, yeah, you can do a stand with just plywood, and have a quite strong one at that. I don't have the precision to cut stuff that accurately my self, but for those who do, they can build a simpler stand with fewer materials, and have it come out quite strong and nice looking.
Believe me I know. Sometimes you just don't have the money for 3/4" oak but with 1x4s and 1/4 you can make a great stand.
Your materials with a 1x4 skeleton behind 1/2" ply is really more not less material.
And I do remember before my skills were where they are now building skeleton cabinets. In fact last year I took apart a solid wood cabinet I built 27 years ago. (solid wood not skeleton) I couldn't believe the sloppiness of the joints and the poor design. Now I build high end stuff as a hobby. If I were to take it apart in another 27 years I know the joints will be right. I won't look back and get that letdown feeling. Every time I visit my mother's house and look at the cabinet I built under the sink I about want to cry. It is terrible. But I built it with wood I had at the skill level I was at. Man I hate that sink cabinet.
The main thing I see with his plywood really is the grain direction.