Depending on their local rules, they may be obligated to investigate any leads coming in from the public, and that can become a massive drain on resources that would be better spent on following up leads they may already have. Psychics, intuitives, and other "helpers" are kind of a pain in the ass this way. Depending on the case, if somebody says, "I've helped find four other people, and last night I dreamt that so-and-so was alive, and cold, and in a big steel pipe in the woods", then the people in charge of the case get to spend a bunch of resources checking out culverts in forested areas. Public missing persons cases always bring out these folks.
If LEO does want to get the public involved, they often have even better tools available, including reverse-911 text alerts.
They may also be operating with a different set of information than they're sharing with you, and may be withholding some information for good reason. They may already have a working theory and not releasing details about what the missing person was last seen wearing may be helpful for sorting out good leads from bad ones.
All that said, law enforcement isn't infallible and mistakes are made in missing persons cases, even by well-intentioned and experienced people. And certainly the grief and frustration and helplessness experienced by friends and family during cases like this should be given more consideration than perhaps it usually is.
But, if you run an ad that has the word "YOU" you're going to have a bad time in FB either by ads getting rejected or the AI straight banning your account.
*: I run well over 7 figures a year in fb.
Why?
Many people already use Facebook posts to raise awareness, but the effect here is that they mostly get shared within their own circles and not necessarily in the location, where it makes sense. With Facebook ads your able to target exactly the people in the search area and ask them to not only keep an eye out for your missing loved one, but also to spread the word. Essentially, you are paying Facebook to show the post to the right people in a timely way.
Most of the money goes towards Facebook ads. We take a 10-20% cut for our services.
Would you still object if outcomes were objectively better?
I say this as someone who really doesn't like FB, and thinks that at least on a napkin it makes sense that by contributing to depression it might contribute to all sorts of negative stuff, including people going missing. That's all valid, but both secondary and kinda tasteless in this context.
Someone looking for a missing person will be happy to hear useful information about any and all avenues they could take. I'm right with you picketing companies and anyone who has a Facebook page instead of an "actual webpage", and whatnot. But people who are worried about someone who went missing? Nah. I get where you're coming from, I respect and might share it as knee-jerk reaction, but think it through. In that situation, you exhaust all options.