You don’t need any supporting base when floating around.

Not to resist gravity, yes. But you need some supporting structure to keep things apart which are meant to be apart, and keep things together so they don't drift away into space. The general frame of the object, so to say. If you don't use a natural crater to support your telescope, you need to create some kind of structure to do that job for you.

since you don’t just have to reach but land on the moon too, I assume it absolutely takes a lot more effort per mass. Unless you can impact the moon at full speed.

A similar thing is true for any point in empty space. It's not enough to get there, you need to decelerate to come to rest when you reached the destination. Yes, when landing on the Moon you need to additionally fight it's gravity. I still think the energy required to leave Earth vastly outweights the energy required for the final approach. After checking [The Tyranny of the Rocket Equation (NASA)] it seems my estimation was exaggerated, but still right in principle. The most energy will be spent on reaching LEO, and landing on the Moon instead of going to a cis-lunar destination is a difference of 11.5 or 14 (total trip costs) compared to 8 for the initial lift. Numbers from the first table.

Either way, this is amateurs arguing what experts should do. The better approach is probably to dive into their documents to understand their reasoning. Even if we'd agree they should build their telescope in space, that would maybe rather hint at us missing some insight.