One could conceive using an insulator on the bottom layer and this is possible but there is little advantage as plated thru holes would be impossible. 3 layer boards are rare but also possible using a 2xboard, one prepreg and one copper layer all laminated
The another exception is a single sided board.
So it is not true that all boards are even sided, single-sided is the best for all consumer goods if possible., not to sacrifice performance or EMC. TVs often use single sided boards with shielded modules. Isn't that odd?
In fact there is very little no cost advantage to even or odd. Least copper is cheapest. In volume it is weight of copper that counts or total copper surface area x layers x oz.
There are many process options in multilayer boards that has little to
do with number of layers and more to do with features. So the
question has a false assumption. In fact any number of layers is
possible and fewer is cheaper. For the best resolution in holes,
thruhole feature etching can be <0.05mm whereas clad etching is worse
due to flow of acid on the surface only. Then final stackup is
controlled by gap in each layer and finished thickness by using
various prepreg lamination options. Old school fabricators used only
double sided boards. Hence even layers. modern fab houses just etch
copper only and add lam to make up the stack and then do plating of
holes. BLind or buried vias add cost significantly with multiple
press and plating operations. So answer is true., it no longer matters
if even or odd
... there are extra costs for excessive holes, excessive drill sizes, excessive milling, blind or buried vias and controlled impedance and extra for polyamide and premium for Rogers Teflon substrates.
I am reminded by my old friend Amit @Sierra that when dealing with 2 or 3 mm tracks and holes, to think of Even layers for sequential processing of laminates to improve yields so a N layer board with interleaved pwr/gnd planes and outside signal planes should be grouped in even numbers if there are many blind interconnects between internal layers. This improves DFM greatly.