"Some" road bikes are limited in maximum tire size. The chain stays are too close together. I avoid hopping curbs on a road bike, but it's OK on railroad tracks and rough roads.

You should test ride some road bikes. I was really surprised 6 years ago when I rode one. It was extremely comfortable, nothing at all like the cheaper 1970s road bikes I rode in college.

And take a look at a cross bike (cyclocross bike--originally for racing on grass). It has the dropped handlebars, but can handle larger tire sizes,and has room for fenders. Many have fittings for a rear rack, too.