The "much deeper" drilling would have to be rougly 900km to get near to the core. No drilling of this scale has been ever attempted on Earth. Lower gravity will make it easier but not much easier, and you will have to have pumping stations from time to time - no pipe will withstand 900km long column of water, even in Lunar gravity.
On top of the difficulties you list there's filling the pipes with water - to make it worthwhile and not cool down to zero within first 100 meters the pipes should have some reasonable diameter. Say, 1m^2 crossection * 900,000m length, times two (up and down) that's 1,800,000 tons of water just to fill it. How do you plan to bring it there?
Sure you might just try to generate electricity deep down there and send it up by wires. This requires the heating->cooling cycle for the water though and while you have heating available locally, cooling might pose some problems. You can't use cheap evaporation, or convection. You're pretty much stuck with dissipation into native rock, a huge grid of thin pipes conducting the heat away into the rock far enough from the "hot zone" to make it worthwhile. The further you get the more water you need.
On the other hand:
- there is no air to disperse solar heat
- there are no clouds to obstruct it
- the dust flies very short way without wind to carry it, to cover the panels.
- there is one rotation per month, so automatic tuning systems are idle most of the way
- the moonquake risks are minimal on the surface.
- there is no need for bulk amounts of expensive materials like water. Quartz is abundant on the surface.
- Sure you have half-month-long night (when you might need to use stored energy or pull it by wire from the other side of the moon... or at least use an orbital reflector to bring it to the panels) but then you get half a month of constant energy.
In other words, if we didn't have the option of abundant, efficient, cheap solar energy we might feel compelled to seek other options like geothermal on the Moon. Currently though, there is simply no reason to pick a solution several orders of magnitude more expensive when you have something so cheap and efficient as solar power.