That method only works for about one season, and then you have to redo it all. I guess if you like gardening redoing the cardboard isn't so bad, but I'd rather focus on the plants and not the cardboard.
Last year, I put down cardboard and mulched - planting strawberries directly in the mulch and piercing through the cardboard. Fast forward a year, now that the cardboard is pretty composted, the strawberries were established last year had root systems in place, broke through the cardboard, and beat most of the weeds. The weeds can't thrive because the strawberries are taking up all the sun.
Side note, using large pieces of cardboard or packaging paper goes fairly quick. I wouldn't consider it hard or time consuming.