For elementary it's only available/set up that way in a few places. Like I know of one school in my entire state that does it, and on homeschooling boards I know of about half a dozen in the whole country.
But a lot of people use the option in middle school, and some use it in highschool (more people just send their kids to community college part time during highschool years).
Many elementary schools ALLOW partial day attendance, but it's not set up that way (like the half dozen schools I know of), so It's cumbersome. In elementary school the rest of the kids are there all day with a single teacher, and there aren't set periods for things (like in middle and highschool) and it becomes a nightmare for teachers and parents... so schools strongly pressure kids to be there full time or not at all. And that's even assuming the school allows it, for many do not.
Middle & Highschool are easy-peasy in most states. You just sign your child up for 1 or more class periods and they attend those classes. The schools like it because they get paid for the headcount, even though the student only attends part time, AND it's not a pain in the neck for the faculty. Need algebra/art/physics/theatre/football/etc.? Just sign up or try out. The teacher or coach has you for the same amount of time they have the other students in the class.
Community College is free for highschool students (to take 100 & 200 level classes) in "dual enrollment" states (I think 36 states have the dual enrollment option, but I'd have to look it up and am feeling a little lazy right now)... so many HS'ers send their kids for 1 of 2 purposes. Either to get their AA/ AAS so they go straight to university as a junior at 17 or 18... or to use their community college hours as their highschool transcript for competetive entry into some of the ivy leagues. This option is losing momentum, though, since many ivies are actively recruiting homeschoolers, and most universities have a homeschool application process which is preferable to trying to transfer in using their CC hours as highschool hours (still, 100 & 200 level classes).