In AZ you can. In the 90s mandatory inter-district open enrollment for public schools was started so that you can apply to go to a school outside of your district. Usually you went to whatever school was in the same zipcode as where you lived and if that school was possibly full you'd go to another within the same zip. Or with open enrollment, you could enroll your kid elsewhere, to Tempe, Mesa or phx whatever, but the only draw back was no school bus would pick you up.

In HS ('99) my family moved a mile up the street but it put us in a different zip. I would have to go to one of the high schools in the new zip code but my mom wanted me to keep my friends and enrolled me in the HS I would have originally went to. I had to take city bus to get there but they had reduced monthly/yearly bus tickets for students you could get from the public library (was like 40 cents a ride back then) It wasn't a long ride tho, my HS was like 3 miles away.