Wood-fired versus kitchen oven

There's a local restaurant with a wood-burning oven. They start a wood fire in the baking chamber and let it burn for hours. When the wood has been reduced to embers and ash, they are swept to the side and the food baked next to them. Unlike grilling over wood, the food does not have a smoky taste or aroma. 

So, what is the advantage of baking bread in a wood-fired oven?

I've been trying to convince the local library to hold a summer workshop to build a mud oven, then use it to bake bread. I think it would be fun and messy group project, but they think it would be dangerous "and why not just hold a break-baking workshop using a regular oven." Any bread-baking workshop is good, but what are there any selling points for using a wood-fired oven?

Janet