Well use certainly reduces the life of the "wear" components (tubes, power supplies, bulbs/lights/projectors, etc.).
That seems like a reasonable assessment that the Wii on the same strip as the TV and still functioning likely means there wasn't lightening damage.
The TV might have just failed due to it's age and use (so unfortunately your Dad is indrectly correct). FWIW, we tend to leave our sets running all the time too, but just factor that in as part of the cost - we don't worry about using something as intended.