The reality is that engine management takes over and unless one is heading towards a mountain one is not going to change from enroute flight to Vx or Vy just to climb by 1000ft.
Also most planes will overheat the engine if climbing at Vx or Vy for any length of time, and one needs to trim for a higher airspeed to get the engine cooling.
In "traditional teaching" one climbs at Vx until clear of obstacles and then climbs at Vy until top of climb. In practice one climbs at Vx until clear of obstacles (which in most parts of Europe is less than a minute or so) and then one trims ASAP to a speed well above Vy to get the engine cooling.