I got the feeling you couldn't just go find a planet and settle it in the Star Trek society of the 23rd century; you needed government approval - and in fact that group would NEVER get it because Doctor Sevrin had/carried a disease (which he got because of the Federation's high tech life support systems), that required him to remain in a high tech/managed environment or he'd die/infect others; so he and his group of followers were looking for the planet 'Eden' because it was outside Federation jurisdiction; and a supposed Earth-type 'Paradise'.
That reminds me: the seemingly ridiculous aspects of TWTE are:
1) The idea that, not merely someone, but
everyone (!) would think that Eden was a real, historical place.
2) That Eden was understood, without need for discussion, to be a planet, in fact an exoplanet, rather than a place on Earth-- where did that idea suddenly come from?
3) And that we somehow had enough information about this inferred planet to predict its location in interstellar space.
Buh-whaaa? The Bible doesn't contain ANY of this information, and that's where the story of Eden is told.
Just as "The Omega Glory" did not tell us how the natives got our Constitution, this is a huge whole in the story. We are not being told something that the story hinges on and the characters take for granted.
I would suggest that when the Space Hippies say "Eden," they aren't referring to the Biblical place, but to the Terran nickname for a legendarily beautiful planet that Federation people have heard about from aliens, and thus have some solid, historically recent information about, but whose location in space has not been nailed down.
So searching for this "Eden" planet is more akin to looking for
Bigfoot, the
Loch Ness monster, or
Noah's Ark, in that not everybody thinks it's worth it. And it's like the 1985 search for the
Titanic, in that the thing is real but its coordinates have been elusive for a long time.