Phase 2 NASA NIAC study for a 1 kilometer diameter lunar crater radio telescope.
The researchers have selected the best crater and worked out how to minimize the weight. They have worked out the main aspects for construction and deployment.
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If you want to create public excitement, why not recruit some James Bond villain billionaire to create some bespoke craters on the moon with a nuclear shaped charge. Sure, you build the first radio telescope using whatever crater you can find, but when you want a specific shape for v2.0 at a specific lunar spot (equator, north pole, south pole), just light off a device left over from the 1950's "atoms for peace" program
You are usually right about Space being the place, but this is an exception, for the shielding reason. Same for solar power, as Criswell LSP shows, perhaps, as there is already a surface there, in the sun, in a vacuum. However, theses exceptions are rare and the general public is so knee jerk planet chauvinist that Space *itself*, esp micrr0g, is ignored entirely.
Launch weight might be the same, but the delta V to deploy it to the lunar surface ISN'T
Now redesign the project to a 100 ton limit delivered by Cargo Starship and assembled by a team from a permanent lunar base. I bet it could have double the diameter, 4X the area, 10X the performance with other enhancements possible at higher mass delivered. Same crater – that’s a nice one.
The launch weight of the radio telescope components is the same no matter where it is deployed. The components deploying and maintaining the structure vary by where and what technologies are used. I would take the "passive anchor" model as an effective lowest possible launch weight, as you would need rockets or maneuverable micro-sats to deploy in space.
But as mirmeemor says, the point is all that lovely lunar rock between it and the signals emitted from Earth.
The reason for putting it on the far side moon is to shield it from the Earth's radio emission. We can get a nice clear view of the universe without interference from the light (radio) pollution. Till they start having to deal with all those pesky O'Neill colonies anyway.
The place to put a dish to minimize weight is in space. Unless they plan to source the building materials from the moon, they will save a lot of deltaV by staying in space. There is also the issue of pointing the antenna to where it's needed. Space wins there too.
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The big news is split of O'Neill Space and Mars stuff in NASA.