My husband has been SAHD for 12 years. A lot of the discussion about SAHP focuses on the benefits when the kids are really young (saving on daycare, being there for the big early milestones), and those are all great, but in my experience the benefit doesn't diminish when they hit school age, because school schedules still assume that there's a full-time parent at home.
My kids' elementary school runs from 9:30-4. There's before and after care available, but it's not at all flexible. You basically have to sign up at the beginning of the year and if your schedule changes, any shifts are subject to availability. That care isn't available the first week of school. There are some free after-school programs because it's a Title I school, but that scheduling is even worse, and we've had issues with our kids being kept afterschool when we expected them home on the bus, or being sent home on the bus when we expected them to stay after school.
Also, since the general culture has shifted away from latchkey kids (or at least, latchkey kids in elementary), we once had an issue where a bus driver make our 4th grader get off the bus even though they had dropped their house key and couldn't find it (twilight at 4:30 in MN). Luckily, a neighbor was around and we weren't far from home, but that was a little scary. And that's not even getting started on all the midday choir concerts, art exhibitions, teacher conferences, etc. that get scheduled completely irrespective of standard work schedules.
