I was under the impression that they have less service costs due to fewer moving parts. Or maybe it comes out all the same since there's less to service, but when something does need servicing it's more expensive than usual.
Tesla does not have a transmission, so there's one thing. Also no muffler / exhaust system.
Tesla does not have an IC engine, but what's likely to fail on an IC engine? A bunch of things that fail often are cheap ($100 - $200): starter battery, ignition coils. Some wear items are often more expensive because difficult to replace: timing belt, water pump, alternator. It's possible but rare that you could have something really go wrong: cracked cylinder head: maybe $2000.
Now what does Tesla have? Electric motor- maybe same failure rate as an alternator? High power electronics- maybe same failure rate as something like an ignition coil? Battery- very expensive wear item.
What's likely to be cheaper is long-term repair costs. No muffler replacements, no leaking head gaskets, no timing belts making an attempt at freedom.... But whether that actually works out remains to be seen.
When he took the Model S in they added that metal plate to the bottom (from that one crash that got a lot of press), swapped out all the door handles for new ones because people online complained that in rain sometimes the old ones wouldn't retreat into the car and changed a few other things I'm forgetting (at no cost).
I can't really think of another car company that proactively adds a bunch of stuff to the car for free as a part of routine maintenance. Of course this is in addition to all of the over the air software updates too.
Adding backup lines to the backup display, on the other hand, to 2 year old cars, that was unusual. It was purely a software upgrade.
FWIW I've only ever changed the oil on my 2006 Ford Focus.
You better change at least the timing belt, transmission oil and sparks plugs if you hope it to keep running well into the future.