Wood is not better then metal, unless ease of use and cost are the main driving factors for your equation. Even with wood routers, the stiffness of the construction is a major factor, and there is quite a lot of flexibility in wood. As a result you have to make more and shallower passes and use a slower feedrate. Another problem already mentioned is movement with humidity changes. Painting the wood really good helps with stabilizing here. But it is possible to make such a router from wood and then be able to make products with them.
A quite nice design is:
https://www.instructables.com/LOW-COST-DIY-500-CNC-MILL/First it uses the square MGN rails, which are supported over their length and overall of better quality than anything with round guides or wheels. Second, it uses simple aluminium extrusions to stiffen up the rails. The rest of the construction is made of wood to keep the cost down and make it easy to manufacture with simple tools. It is also an adaptation of the routers made by Sorotec. But Sorotec is all aluminium, more presice / stiff but also much higher in price.
The version from "Bootec" (below) is also very similar, but it uses a bit too much wood to my liking.
If you want to improve these designs, the first thing is to make a box section out of the gantry itself. Ideally you take 4 pieces of angle steel and put those in the corners of a box made of 4 slabs of wood. Or you only put two pieces of steel on the backside, as the front already has the two steel rails.
Next improvement will be to stiffen up the vertical legs of the gantry. Just gluing two slabs of wood together quadruples the stiffness, but better is to add steel or aluminium strips. Just gluing steel or aluminium strips vertically over the legs (both inside and outside) Aluminium is about 1/3 the weight of wood, but Youngs modulus of Aluminium is also 1/3 of that of wood.
Next improvement would be to add some concrete inside the bottom box. Filling the whole box would make it heavy, But pouring a "beam" around the perimeter, and adding a diagonal or some slanted cross beams is a good compromise. You can use UHPC or Epoxy granite, but even regular concrete will work almost as well. But with regular concrete, do add some rebar in it, just as is normally done with any foundation.