Beyond fashion preference, your choice of shoes might seem insignificant in the urban environment. On smooth, flat, even ground, you'd be right. Open toed sandals, or light weight shoes made from a breathable material are a great choice for wearing around town.
But once you leave the well maintained footpaths of suburbia and tread into the countryside, your choice of shoe becomes a little more important. A sturdy sole with a solid tread pattern is far more practical than a smooth soled office shoe. A durable sole stops sharp objects from penetrating your foot. (I learned that the hard way as a teenager when a 6 inch rusty nail went through the sole of my sneaker, and into my foot).
The lightweight, breathable material used for sneakers works wonders when you're running time trials on the track; but will do precious little to protect your foot from sharp sticks or jagged rocks when you're climbing over rough terrain.
Boots that come up over your ankle will help prevent an injury if you are unfortunate enough to roll your ankle (yeah, I learned that the hard way too). And don't forget, snake bites tend to happen on the lower portion of people's legs (leather boots to the rescue).
Even from a self-defence perspective, boots make a lot of sense. Lightweight sneakers will provide your feet with about the same amount of protection as a pair of slippers.
Hopefully, the next time you head out from the urban environment, you'll be a little more mindful of your choice of footwear.