It is easy to get obsessed with heritabilities when you start working in breeding and genetics. The idea that a fraction of that variability we are observing can be explained by pedigree (or family structure or clonal differences or whatever) is appealing. It gives us an idea of control: there is a whiff of causality in our work. If the trait I care about is heritable THEN I can successfully breed for it.
However, we need to remember that it is a fraction of the variability we care about. If there is little variability, there is little room to select farther to the right of the distribution for the trait.
A typical example in trees would be stem diameter vs basic wood density. The heritability for density is, on average, around 0.6, while for diameter is 0.2 in a lucky day. However, the within-site coefficient of variation for density is about 8% but over 20% for diameter. Much more room to move in diameter.
Nothing groundbreaking, particularly if you have been working for a while. Just a handy reminder if you’re a newbie in breeding things.
Gratuitous earworm: In my head, “more than heritability” sounds like the famous More than a feeling.