Hitting all your points in order:
1) 1 million dollars is a lot of money to come out of nowhere. It's simply dishonest to pretend that isn't a life changing amount for a middle class family. At the very least it's going to be like you said- modest home paid off(100-500k), car loans all paid off(50k), and student loans paid off(300k if your kids went to expensive schools and you have 3 of them). I'm really not seeing why anyone should be entitled to never work again simply because their parents made a lot of money. (With that said, my parents didn't choose to bury themselves in debt and could have retired instantly if they received this inheritance when combined with the investments they already had)
2) It's absolutely a lottery. Trying to cloud this issue with "oh well the parents potentially weren't there as much and that emotional cost is easily worth a few million" is disingenuous. It makes the assumption that money has no influence on the quality of the child's upbringing and "time spent with kids/day" is the only metric worth mentioning.
3) Being taxed when you're dead isn't a tax to me. At all. I understand this is a personal opinion but you should have the same understanding regarding your own opinion here. When I'm dead I no longer feel entitled to anything I gained in my lifetime- it's not like I'm ever going to use it again. I also don't feel my kids are entitled to it just because they happened to be born (effectively via lottery) to me.
To suffice:
Let the fruit of my efforts benefit society/humanity as a whole. It was my goal in life and ought to be in death.