I'd support allowing 16-17 year olds to invest as long as a parent agrees. I don't think restricting to the fortune 500 companies is necessary. Maybe just limiting the total amount of shares bought within a timeframe to a certain amount.
I disagree with a fact a parent needs to agree. This is to start limited trading without the need for a custodial account which a bad parent can withdraw from too along with the child
However I do agree with the second idea rather than Fortune 500. I admit my line there wasn't perfect and your idea is probably better. It basically prevents all waste of money in penny stocks.