Like many things in social contract, the answer is - okay to a reasonable degree, but extremes should be discouraged / forbidden.
Some concrete examples: annual limits on gift taxes, inheritance tax beyond a certain estate size etc. Policies which will level the playing field between rich and poor kids:
- very high rate of inheritance tax beyond $1M estate (some reasonable adjustment for inflation)
- no legacy based admissions for any university benefitting from govt money
- funding schools strictly at state level; not allowing local district to fund extra school activities in any way (because that is prone to gaming)
- CA specific: disallowing inheriting tax basis for inherited homes (one of the most stupid aspects of Prop 13 and CA housing policies)