The most commonly cited reason for a lack of summer test dates is the limited availability of facilities and staff when school isn't in session. Most high schools are closed during the summer, so setting up test centers is more difficult. It's also harder to get teachers and counselors who normally proctor the tests to show up for these administrative tasks during the summer when they're supposed to be on vacation.
Additionally, the College Board has said that there seems to be an advantage to taking the test during the school year when students are actively engaged in learning. Most people's academic skills are a bit rustier in the middle of the summer.
Despite these reasons, there have been many calls for the inclusion of summer test dates. The counterargument to the College Board's position, which relates to the problem you cite, is that students are already inundated with other work during the school year. It might make more sense to have summer test dates to avoid distractions and burn out. Still, the organizational challenges presented by this proposal when the SAT is taken by millions of students worldwide have caused the College Board to avoid developing any plan to administer the test in the summer.
Source: https://www.thecollegesolution.com/why-you-cant-take-the-sat-in-the-summer/