Will my DIY wood and PVC cat cage hold up?
I think this will be surprisingly much harder than it looks.
Making two four foot squares isn't too bad, you could make a half lap joint.

Drilling the holes isn't too bad, you could clamp or temporarily nail the top and bottom together and drill through both so the holes line up.  I think it's going to be almost 100 holes if you use 3/4&quot; PVC.  You could go with 1/2&quot; or 3/8&quot;, either would be more than strong enough, and would let more light through for your cat.  It would be more holes, but smaller holes.
Getting a friction fit between the pipe and the wood will be pretty hard, the differences between won't fit, friction fit, and loose fit are tiny.  It might be hard or impossible to find a wood boring bit the right size.
Without a friction fit, the whole thing gets a lot harder to do and at this point I'd scrap this design and go back to the drawing board.
Suggestion, design inspired by

maybe it would be easier to build this with the 2x4 top and bottom frames built with the 2x4 on edge, with simple butt joints at the corners, and vertical strips of wood spaced 1&quot; apart.  Maybe something from the moulding aisle, like a 1/2&quot; x 3/4&quot; pine strip.  You could use a heavy duty stapler to drive little brad nails to hold the strips to the frames.  The strips don't need to be that strong, their strength will be in numbers.
Not saying this won't still be a lot of work and trouble and unlikely to come out right as planned on the first attempt - that's just par for the course.