It certainly is cheaper with modern batteries. With the Tesla model S people have already put over 100K miles on the car and they're seeing less than a 5% loss of range. I'm at about 50K miles in mine and have not noticed any reduction in range or performance. The batteries are rated for 3000 charge/discharge cycles which equates to well over 600,000 miles.
Mechanically the system is far simpler than an ICE car. There are far fewer moving parts. The motor is lubricated for 12 years, instead of every 6 months and 5K miles. There is no transmission, no spark plugs, no belts, fuel pump/filter, etc, nor the huge myriad of other moving parts. There's no head gaskets to go, timing belts to slip, no piston rings, fuel injectors, catalytic converters, oxygen sensors, etc. There is a cooling system, though it is dealing with far less thermal stress than a gasoline engine.
Another thing is that the cost of running the car is a lot cheaper. I pay $50-60/month for electricity (at $0.119/kwh and drive around 1000 miles/month, and this is a big car and I don't drive like a grandma either. None of my power comes from coal. Most comes from natural gas, nuclear, hydroelectric wind and solar and a bit of geothermal, plus I have solar on my roof. As time goes on the grid is getting cleaner, since it's actually cheaper now to install wind or natural gas compared to coal, which is growing more expensive as all the large seams are used up. Also as time goes on the electric grid gets cleaner as older plants are shut down and replaced with more efficient plants that burn more cleanly. In fact, today a lot more coal plants are being shut down than are being built. Natural gas is cheaper and produces half the CO2 and a fraction of the other nasty stuff coal plants have to deal with and wind is now cheaper still in many places.
This chart from here shows how things are changing. Notice the very rapid shift in recent years.
My previous car was a Prius. It's still going on after 10 years with the original NiMh battery pack, and the Prius cycles the batteries a lot more than my Tesla does. In the almost 4 years since I've bought my car they've improved the power density, reliability, performance and reduced the cost quite a bit. My P85 is now available as a P100D (100KWh in the same form-factor as the 85KWh battery in my car). The electric motor has no brushes to wear out nor even any rare-earth magnets to worry about, being an induction motor. Even the brakes get quite a bit less use than those on an ICE car since much of the braking power goes into recharging the battery.
As far as regular maintenance the only things that need to be dealt with are:
- changing cabin air filter
- change wiper blades
- check/change brake fluid
- check/change brake pads (far less frequently)
- change coolant (though far less frequently)
- wheel alignment
- rotate tires
- replace tires
All of these are similar to a gas car, though notice what's missing.
- No engine air filter
- No oil changes
- No timing belt or any belts
- Less brake maintenance
- No power steering pump (electronic, though more gas cars are doing this now too)
- No engine-driven AC compressor to start leaking (sealed electric compressors tend to last a lot longer)
Notice I didn't say anything about the battery. The battery is under warranty for unlimited miles, 8 years, though I suspect it will last a lot longer than 8 years, and when it comes time to replace it, the cost keeps dropping, not increasing. EV car batteries are not the same as cell phone batteries and they're not treated like cell phone batteries. Cell phone batteries are optimized to be thin and as much capacity as possible, then when you charge your phone it usually charges it to 100%, which is very hard on the battery. EVs typically don't charge over 90%. While I can charge my car to 100%, it's very rare and typically I only charge to 70-80%.