I have seen many embarrassing situations after an ATC request to reach a level by zzz point.
On one occasion, we were climbing to 370, our optimum altitude, and we got a "expedite through 360" ATC instruction.
the pilot reduced speed too much, and after the initial increase in rate due to the energy trade, the airplane got stuck at green dot and a very low rate of climb, and green dot increased as we climbed so we had to actually accelerate to maintain it, and rate became less and less, till it was zero… while crossing 360.
And it is not easy to get out of that situation! The airplane will not accelerate easily, specially 320s which are very limited in thrust. It was so embarrassing, we should have requested a descent to 340, but after a loooooong time, feet by feet, we managed to leave 360. I'm talking about minutes, here.