The answer is we’re not 100% sure why, but there is enough evidence to support a generalized recommendation to wait. Stability is likely part of it, but there is likely more to it.
Some hypotheses include availability and diversity of bacterial populations, diversity and availability of microorganisms and microfauna. Chemical interactions between corals/plants etc. I’m sure there are tons of other possibilities as well.
What we know for sure is new tanks lack biodiversity in general, even if they are stable. That may be why anemones often die even in young but stable tanks. Typically, when you hear success stories about new tanks and anemones you find out the new tank used mature rock which will significantly expedite biological development in your tank.