It's not really schadenfreude, it's just "tough shit".
People who aren't rich are more used to having things not go their way, to changing what they buy and where due to cost of living, to wearing more layers inside in winter, to cutting their cloth smaller and smaller while the rich just absorb the cost and buy what they've always bought and set the thermostat to its usual temp for a bit more money.
Most rich people will absorb this cost too. Most tales of working five jobs to put their kid private, of pushing average kids out of the good state schools is bollocks.
The thing that the rich don't want to admit, is that part of why they pay private fees is to avoid you and your child.
My sister did so well in the 11+, she got a free pass to a single sex school that was 90%+ fee-paid.
My parents weren't what you'd call poor by any stretch. But we never had a proper pool, designer clothes, or people who "professionally" decorated our house for Xmas. So my sister and other actual clever girls were "poor" and singled out and bullied for it. My parents also found it hard to get in with PTA parents.