Heritability is the proportion of variance in a trait that can be ascribed to genetics. So if you increase or decrease the total variance in the population u change heritability by definition. Eg. Split the pop in half and give one half less food - that half will be smaller (eg shorter in humans) and variance will increase thus the heritability will necessarily decrease.

Yeah, it's not immediately obvious, but if we created perfect utopia where conditions are ideal, perfectly matched for given individual, heritability would be 0%.