Even a 100% estate tax wouldn't do it, the disparities in opportunities (access to and expectation of education, social contacts, …) don't go away, nor do provisions set up during life (companies, trusts, …).
Not to mention other genetic differences, such as physical health, attractiveness, height, etc.
Do you mean non-genetic? There may be a measure of genes, but in the aggregate these will more likely be linked to nurture (access to food, healthcare, …) than nature.
Yeah, obviously "in the aggregate" everyone is average-looking and of average height. When looking at a single individual in a first world country genetics will be the primary determinant of their height and physical attractiveness.