Cameras that have both a mechanical and an electronic shutter usually use the mechanical shutter to take pictures and the electronic shutter for video and live view.
This is simply because the designers of that camera decided to use a mechanical shutter (there are some very good reasons to do so, the pros and cons of mechanical vs. electronic shutter are outside the scope of this answer) - if the camera designer wanted to use primarily the electronic shutter they wouldn't add the mechanical shutter into the camera to begin with.
The electronic shutter is used in video mode simply because it's faster and opening and closing the mechanical shutter 30 times a second is crazy.
And you are wrong about the mechanical shutter being like a candle - there isn't anything there that is spent when you use it, the shutter is a small, complex mechanical construction with fast moving parts and every mechanical device eventually fails.
Just like the engine in your car (or the spinning disks inside your hard drive) the shutter just works until one day something breaks.
Generally the shutter in a modern DSLR is designed to out last the camera body - that is, you will want to replace the camera for a newer better model before the shutter fails - higher end cameras have more durable shutters because they are designed to be used by pros who shoot all day every day, etc.
You can just do an eBay search for "Canon 350D" and see a whole lot of used entry level cameras that were produced on or before 2006 (when the model was replaced by the 400D) and still work today with their original shutter, for fun you can compare their spec to the newly announced 650D and think how would you feel if the shutter of your old camera failed after several years (8+ in the case of those old 350Ds) and you had to upgrade to a significantly better camera.