What would it take for Fox to release full AMW series?

Freedom of Information Act wouldn't work because Fox is a privately-held entertainment company. FOIA only works for public entities.

As for why it won't be released, I have a few ideas. For one, the show had very little rerun value. This was actually a reason for the show's initial cancellation in 1996. This differs from Unsolved Mysteries since not every UM case was a fugitive or missing person. UM included cases on UFOs, ghost stories, historical mysteries. That provides entertainment. UM also had a massive fanbase with people who would always talk about the show all the time, long before the internet provided a place for it to happen. AMW didn't and doesn't have that. Outside of the people who frequent this forum, I've really never met anyone in real life who watched the show.

There's another factor, too. John Walsh wrote in one of his books about a missing child case the show profiled where the little girl was covered. He used a pseudonym when discussing the case, saying that the girl's parents asked that her real name not be used anymore. I'm unsure how many cases there are like this, but I suspect there's probably a good number of since-recovered missing children - especially those that were not as well-known - that don't want their real names revealed.

You'd also probably have to add graphics to the show to update whether a fugitive/missing person/unsolved case is no longer active. That takes time and money. You'd have to edit out the phone number since the hotlines are no longer working. This would also mean you'd have to edit it in a way that removes John Walsh saying, "If you've seen.....call our hotline."

AMW had probably about 1100 episodes (or close to that amount). That would take a lot of effort to go through every single one of these episodes and edit them so that they'd fit to those standards. Not to mention they'd probably have to work out some deal with the crew in order to air it.

It's probably just too complicated. It's easy for us to say "Why doesn't this happen?" but UM was a show that was meant to be reran. AMW wasn't.

^ This is partially what I'm trying to do with a project I'm working on. My goal is to determine every known profile date or approximate profile date for every known case on the show, and even some unknown cases.

Edited to add: We have some big holes, unfortunately. Generally everything from November 1998 onward we know, and there are quite a few profile dates from 1996 and 1997 we either know or we can make some educated guesses about. Most of the fugitives profiled from 1988-1990 are known (though there are some holes, as evidenced by the recent 1988 episodes that recently resurfaced that revealed Stephen DeLorenzo was profiled more often than was initially believed). One of amw.com's previous incarnations included fugitive profiles that included the dates they were profiled, but even those aren't always accurate (there's at least a couple fugitives that list the dates of their Final Justice profiles in addition to their AMW profiles, which isn't really helpful). Plus, as we've mentioned, a lot of episode summaries neglect to mention missing children that were profiled (for example, until their episodes resurfaced, we had no idea missing children, and later murder victims, Amy Mihaljevic and Jessica Martinez, were profiled on the show when they first went missing, or that Billy Ray Riggs/Hilda Sims' victim was profiled on AMW as a missing person before her body was found).