If you are a good trader and have the right emotional temperment and know something a bit more than the Joe who takes his taxes to a preparer, I say that direct participation in securities beats a MF most of the time.
For young children, the tax exemptions in a UTMA is a major advantage, guaranteed, and portable across different types of investments.
I kept a MF(s) and a selected growth stock(s) as foundational. On top of this foundation you can build either/or MF or stocks/bonds. If you are an active trader then you would probably have more stocks. If you are not an active trader and know very little about stocks a parent would be more into MF.
In your original scenario, I think you are ignoring some tax issues. If the trading (the nonqualified, stock) program is performed in an UTMA, under 14, there is the $850 exemption, $850 under minors tax bracket, the cap gains of 5% max (current)on top of $1700, 0% fed tax on dividends on securities held after 1 year. Trade loses that offset gains.
... Assuming no losses. your first year of $5000 investment, 10% gains ($500) would see 0 fed tax. The end of second year, you will see $1050 in gains for total of $11500. Child's taxes would be only on $300 at 15% = $45. Your basis is now much higher which means unrealized cap gains will be taxed when realized will be lower.
As your stock (could be in MF) portfolio grows you can manage the taxation and utilized cap losses by moving some of the gains to a 529. The kiddie tax rate has been extended to age 24 but with close attention, this is an issue for inattentive parents.
Please consult tax experts. My knowledge is getting too dated.