We've never had a physical required for school, just proof of immunizations. But, if there is a health issue that the school will be dealing with, they required some paperwork regarding those issues.
Sometimes this paperwork is ridiculous and redundant. DS has an epi pen stored in the medical station at school (due to getting allergy shots in the morning before school). The pens come labeled with the prescription and directions for use, but I still have to have a physician-signed form detailing the dosage and directions for use. Overkill if you ask me since all that information comes on the pens.
My kids still get their vax at the health department, they just bill our insurance. I find it easier to get an appointment there, and much quicker turnaround time. I prefer it to the doctor's office.
Our son had to get a physical every year for football starting in first grade. We schedule these at our company clinic because they are free there. We do have to work pretty hard to get an appointment with our preferred provider in a timely manner so we have to schedule almost as soon as school ends the previous year.
Physicals were not required for baseball, softball, soccer, cheerleading until 7th grade, I believe.
Interesting how differently states and school systems manage these issues.