Does your school have 1/2 day kindergarten classes?
My mom taught kindergarten for several years. Her school had a morning class & an afternoon class. The two were really lopsided. The morning class had 20-something students, the afternoon class was at least 1/2 the size.
The school offered to switch kids from morning to afternoon, but none of the morning parents did. It had to due to day care issues. The parents could drop the kids off on their way to work & then "after-care" would pick them up.
Also, if your school has 1/2 day & the public school has full-day kindergarten, parents are probably opting for that, again to save on day care.