You have to balance two factors - rim strength and wheel stiffness/rigidity/flexibility.

Curbs, Potholes, Impacts:

You need a rim that resists bending. A wheel resists sharp impacts with rim strength and basically only rim strength. If you've ever bent the sidewall of a rim (imagine using a bottle opener on a bare rim and you get the idea) you know what I mean - a million spokes wouldn't help if the rim itself deforms. Some people would argue that having a lot of low tension spokes would help the rim flex and absorb the impact and therefore prevent the rim from bending, but after checking, servicing, and repairing hundreds of wheels, I've found that a stronger rim is absolutely necessary if you want a stronger wheel.

I've built some very light rimmed but many-spoked wheels (like a 36H 280g alum tubular) and the wheel is easy to true but easy to knock out of true. I bent pretty much all of them. Bent.

If you want to avoid bending rims on potholes and curbs then it's the rider's technique that needs to be upgraded. You need to be able to unweight your wheel going over a pothole and to lift the wheel when going over a curb. The only curbs I can't get over are the ones where my chainring hits the curb and I get stuck. With a little bit of practice you should be able to bunny hop a pothole and do a one-wheel-at-a-time over a curb.

Flex/Efficiency/Comfort:

Using more spokes gives you the option of lowering each spoke's tension. You need a certain amount of tension within the wheel to maintain structural integrity. If you have 12 spokes you need really, really high tension on each spoke. This means that the spoke attachment points need to be reinforced, you need to use the exact tool to true/tension the wheel (using a green spoke key instead of a black one will strip the nipple for example), spokes break more frequently (since they lose elasticity with tension), and when a spoke breaks the wheel goes way out of true.

Note: if the rim is super strong then you can break a low spoke count wheel's spoke and still do a ride. I sprinted on a 15 spoke front wheel after breaking a spoke early on in the race. The course includes a 45-50 mph descent and after some experimentation I found the wheel was okay.

Using more spokes means you can reduce the tension of each spoke and still maintain wheel strength. If you lose one spoke you lose less of the whole support system. I've worked on 48 spoke wheels for BMX bikes where the kid has broken 3-4-5 spokes and the wheel is still true and still strong. I've worked on 48 spoke touring wheels (700c) where the rider finished some Southeast Asia tour with a couple-few broken spokes and while carrying 30-50 lbs in panniers on the back. Again, the wheels were fine. Even my own personal mountain bike has a 31 spoke rear wheel - it uses 1.8mm spokes and I haven't bothered trying to find the proper replacement, and the spoke broke before I got the bike maybe 10 years ago.

With more spokes and less tension the spokes last longer (because it's under less tension - think of a rubber band that's either stretched all the way or only part of the way - which one will last longer?), the rims tend not to crack etc (because the spoke holes are under much less tension), the wheel can be softer (lower tension spokes), etc etc etc.