[pdar4123]

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.

[readthenotes1]

This author seems disagrees with you:

"Heritability does not indicate what proportion of a trait is determined by genes and what proportion is determined by environment. So, a heritability of 0.7 does not mean that a trait is 70% caused by genetic factors; it means that 70% of the variability in the trait in a population is due to genetic differences among people."

https://medlineplus.gov/genetics/understanding/inheritance/h...

[krzat]

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%.

[robwwilliams]

No. Then the fraction of population variance attributable to genetic differences would tend to increase and heritably would also increase.