I have a Opt Lasers 6W laser and by using air-assist at around 0.5 bar i can cut through hard plywood like birch in 5-7 passes with very clean cuts (1000mm/min speed) depending on what lens i use. 5 passes with uSpot lens and 7 passes with G7 lens.
You can see some wood work made with Opt Lasers 6W laser from eg. at www.instagram.com/cncpaja
By air assist i mean a 1-2mm pressurized nozzle that blows air downwards. It makes the cutting much more effective by blowing the smoke away. Without air assist the smoke intercepts very hard the laser and thus reduces the cutting efficiency.
And you should just make sure not to use any exterrior plywoods since they use black glue which prevents cutting even with co2 lasers. Always use interrior plywood which uses white or transparent glue this is easier to cut through. ( i dont know why the glue color is the issue and i think thats not the issue but the black glue is just tougher than the interiorply glue)
you can find the laser from here if you are interested in it.
and here is the air-assist