There are missions all the time to recover remains of meteoroids that didn't burn up. https://www.nasa.gov/feature/goddard/2018/antarctic-meteorit...
But people don't exactly go running around saying that they're trying to find Thor's spaceship from that time O'Neill, Carter and Teal'c blew it up. (sorry huge Stargate fan) Even if he finds nothing, will the conspiratorial people believe that? Or, will they believe that The Powers That Be hid the Top Secret Alien Technology from the enterprising scientist?
He's adding fuel to the conspiratorial fire.
You do make a good point about conspiracy types, but I don't think it's necessarily his responsibility to educate everyone out of that. The best way to let the air out of that particular balloon is to send a small rover to the moon and land it near the original Apollo site, and then just drive it around beaming back pictures of stuff on the moon and attractive hi-res pics of Earth on a daily basis.
Does it break any new scientific ground? Nope. Will it do wonders for public awareness of/engagement with science? Hell yes.
A simpler example again than a rover would just be installing a camera on the Moon that points back at Earth and beaming a high-res whole planet image in real time. The lack of imagination in existing space projects is just deplorable. If you want a bigger science budget, a planetary selfie stick will pay off in spades. Flat earth people will dry up and blow away after a year of people being able to look at the planet they live on and see weather patterns, wildfires etc.
He has had such an amazing career and has done such great work that it physically pains me to see him slide into Nobel disease this way. https://en.wikipedia.org/wiki/Nobel_disease He has always been fascinated by the search for extraterrestrial intelligence, but he was such a reasoned person who proposed great techno signatures like looking for pollution as a means to detect industrial-age civilizations.
It’s like watching a giant stumble and hurt himself on purpose. And it gets worse when non-technical people come up to me and ask, “have you heard of Avi Loeb?” Instead of being a beacon for enlightenment, he has gone down the path of spreading conspiratorial ignorance. It is painful to watch such a great career fall this way.
And no, based on my conversations with my professional astronomer friends, no one inside the field takes him seriously anymore. They don’t laugh at him either, they just don’t take him seriously. It’s probably why he doesn’t seem to have a more prominent role with the JWST. Interesting projects don’t want to associate with him anymore. It’s sad.