Fad? Go back a few decades, and road bikes with 28mm and 32mm tires were a fairly normal thing.

More tire doesn't necessarily take more to push.
Assuming a wide tire and narrow tire are otherwise constructed similarly, the wider tire will add a bit of weight and possibly air drag. But, it enjoys more favorable rolling characteristics, especially when low inflation pressure is desired.
On smooth surfaces, the overall effects of tire width are small enough to be difficult to measure. The rougher the surface, the squishier a tire needs to be pumped to roll smoothly over it, and the more advantaged high width can become. The pros use tires like 28s in races like Paris-Roubaix because there are critical moments in those races where wide tires take tangibly less power to push.

Do you mean that you ride a mountain bike for road riding when it's wet?

Riding a mountain bike on the road isn't a good gauge of the effects of tire width. Mountain bikes are usually somewhat sluggish on the road even if you install fast road tires: for instance, it's harder to hold a nicely aerodynamic posture on a mountain bike than a road bike. Also, while MTB tires do tend to be slow on the road, their knobbies and beefy construction tend to be more responsible for this than their width.