it's not the moving parts in the engine that cause most of the maintenance costs, it's all the rest of them, like suspension, steering, brakes, air compressors,
All EVs will require most of the above (but remember, the only air compressor is on the a/c). There is no clutch and no conventional auto-transmission. Braking though is partly friction but is also electric (regenerative), this should lengthen the life considerably.
I know what you are getting at but internal combustion engines certainly do need additional maintenance. The issue is at the moment is that we know very little about the total lifespan. I know someone who bought a Tesla Roadster and is very happy with it. It has received no unplanned maintenance but then it is just a couple of years old. No modern car should have a problem that early. Five or ten years on may be another story.
One of the interesting tendancies is that to balance the weight of the batteries, many manufacturers have chosen much more modern materials, so we see aluminium in the Tesla and carbon fibre in say the BMW i3/8. This costs more, but has long term benefits.
I would agree that the battery is and remains the most critical element and this has to be accounted for in any TCO calculation. Again, we do lack information, particularly on the realistic trade in possibilities for a battery. For example, whether it can be reconditioned rather than completely remanufactured? These questions will be answered over the next few years and lets be honest, not everyone is going to rush out and get an all electric vehicle and for many, it isn't even that practical. For all the indentations being made particularly by Tesla, there are many more ICE vehicles. Over time, though there will be further cost reductions and more people may decide to switch.
As more EVs are on the road, there will be an increasing need for a dealer network to provide the necessary downstream support. At the moment, we are talking niche, so to require dealers when there is such a low volume seems impractical.