There is a shortage of certified/credentialed high school math and science teachers – I suspect that factors into your cousins pay.
There are other factors – if your cousin has an advanced degree, that ups the base pay. Years of service ups it.
Your cousin may not do outside prep work – but my sister (elementary school) works about 80 hours/week. I think there are some lazy teachers and there are teachers like my sister… You can’t lump them as all the same and generalize.
My sister left a much more lucrative career to follow her passion to teach. She’s pretty much maxed out on salary and still makes about half what she was making in the private sector.