Not disputing that there are shitty companies out there, but I worked somewhere that did this exact thing (10+10 to 15) but it was explicitly said that sick days don't burn PTO. If you're sick you don't work, paid, and if it's more than 2 days in a row you need a note. Basically, treating the employees like adults.

If more companies did that people would be happier and more productive across the board.