And at L2, we'll never be able to upgrade it or even service if something were to go wrong before end of scheduled mission. Something on the moon would be much more accessible for upgrades or basic servicing missions. Even with 2 week on/2 week off schedule, it would be so useful. During those 2 weeks off, it would be charging its batteries. Never would it suffer from cloudy nights.

OTOH, a trip to the moon requires about 10x more fuel than going to L2. Although I suppose a moon telescope could synergize nicely with other lunar activities

Edit: I think I misread the table I was looking it, it's more like 2x or 3x instead of 10x, and that assumes a start from LEO

There are and have been probes and observatories at L1 and L2:

https://en.wikipedia.org/wiki/List_of_objects_at_Lagrangian_...

The dark side of the moon would be much better for a telescope array; given that the moon has no atmosphere and isn't seismically active, you could form a massive, scalable array with incredible resolution.

Is the Earth that much of a hassle if we built on the near side instead of the far side?

Perhaps for radio astronomy?

Or build it on the far side, near the poles, with a solar array just across the pole -- perhaps that way you could have solar power all year long.

Most large telescope arrays (that I know of) are for radio astronomy, largely for geographical reasons (as far as I know).

Earth is a source of noise throughout the electromagnetic spectrum, so I think the benefits of building on the far side (eliminating Earth noise), will likely outweigh the costs (limited/more costly bandwidth).

I think a mixed array, consisting of "radio" and "light" telescopes could present very interesting possibilities, especially because you could dynamically allocate sparse sets of the array to different tasks.

All of that being said, I am an engineer (with an interest in array signal processing), not an astronomer.

Sunlight is reflected from earth too.