YES! Exactly this.

Passing down of beliefs and behaviors is almost more valuable than passing down money.

You're embedding positive or negative behaviors into someone's personality.

1>Passing down the belief that education is valuable

2>Passing down the belief that investing in the future is more valuable than short term spending.

etc.

Also having resources in general is a massive benefit. 1>having security allows wealthy kids to take more risks/reap more rewards.

2>More free time to learn and advance themselves

3>ability to take low paying jobs purely to make connections/build job skills

4>Status is a language that every one understands at a primitive level and so just getting more respect in general which means better promotions, better mates, etc.