They're typically on the side of the road for the same kinds of reasons as any other cars - people stopping to fidget with phones or stuck with flat tires.
It's reasonable to expect (and reality appears to deliver) long and low-maintenance life from an electric vehicle [0]. There are, of course, issues of keeping the battery warm enough and cold weather climate control. One of the big advances in the Model 3 is using a heat pump for heating where previous models (and most other electric cars, like the Bolt that I drive) use a resistor.
Further mechanical improvements in insulation and thermal management will probably continue to push cold-weather performance quite a ways further. It is, however, always going to be a challenge. Your ICE vehicle produces quite a huge amount of waste heat which can be redirected to the cabin or the glass. And, of course, they're not completely immune to the cold themselves. Places with really serious winters have parking spaces with electrical outlets for engine block heaters. Those will continue to have utility in an electrified future to keep batteries warm and charged.
Personally I'm very excited to see urban delivery trucks electrify sooner rather than later. They're doing a lot of stop-and-go and idle a lot. And they don't drive very fast. So they're super-obvious low-hanging fruit that will really help reduce noise and air pollution in cities. Plus, cargo loading times are long enough to significantly mitigate charging times. Mid-range last-mile delivery in rural areas will be a little bit harder, but still seems plenty achievable with technology we have right now. Long haul seems more difficult and the benefits over a hybrid less clear.
In all cases, however, there's no excuse for being stuck on the side of the road for want of energy. All road vehicles, regardless of their source of energy, indicate how much they have left. Running out is an operator error.
I've never seen a Tesla on the road. I'm not sure they're made in enough quantity or sold across enough geographies and demographics to measure anything technical by collecting anecdotes.
I am told it is. This is by a couple UPS drivers. They could be telling my tall tales. I can only take them at their word. I will ask them to get pictures next time they see this.
Is that common in your area? I do live in the city, but in my entire life I have never seen a Tesla on the side of the road.