I'd be the moron that spent $250 for the wrong bat. I'll stick to googling the bat before I buy it to confirm until I am seasoned enough to know the difference lol.
The difference between a good composite and cheap alloy is dramatic at any age. Certainly in any kind of travel ball or even all-stars your kid is going out there at a disadvantage without a decent bat. Still needs to be the right size and weight but that is totally independent or materials.