Looking for a X axis stiffness. Plywood is cheaper than bigger smooth rods, rails or aluminum extrusions so why not use it more?
Because all things considered, wood warps. Changing the dimension of the printer is NOT a good idea if you want your prints to be straight and consistent.
Heat change gives different contraction - expansion
Solid metal will probably perform better over all, but given how easy wood is to work with and how cheap and readily available it is, it probably makes for a perfect boot-strap material. My little cnc that I mill circuit boards on is all particle board - http://www.flyinglow.ca/flyinglow/cnc-machine/2013/02/
Here’s a PCB (MCB? - MilledCB) I made with the little wooden mill - http://www.flyinglow.ca/flyinglow/2013/04/mpxv5004g-breakout-board.html
I like the way you clamp and fix the rods. 
That’s the whole point of plywood, Mike. Plywood doesn’t warp.
And to respond in a more positive way, if the bearings were inserted into metal plate (say 1/8th" Aluminum plate), then the plate were attached to the plywood, you’d greatly constrain dimensional change. Aluminum is relatively easy to work with, metal drill bits and a metal blade in a jigsaw and a little determination could do it.
To add some more constructive thought to the discussion - am I correct that the big enemy of wood is humidity? Plywood attempts to counter the expansion / contraction by alternating the wood grain. Are there different materials that handle moisture better / worse? (There is a larger cnc router designs that call for MDF as the material). Your design in this picture has strong looking boxes and ends - but that long beam of wood might be a warping point. Would adding a plate across the top help?
Plywood used in project is high quality waterproof plywood. It is true humidity is an enemy of wood, especialy this one used in laser cutters - water based glue.
In the and there is space for linear bearing and nut. @Alex_Wiebe I’m thinking of bottom(top) plate which could give more stiffness. But now I’m happy of results.
I don’t want to overweight Z axis.