For the most part, it’s a good idea to do at least some of your running in light, flexible shoes.
What’s been termed “minimalism” over the past few years is really what most runners naturally did before the shoe industry started pumping shoes full of technology, dramatically elevating the height of the midsole, and creating large differences between the midsole height in the heel and forefoot. Before shoes started resembling moon boots, most runners trained in low-to-the-ground models that hugged the foot. Combine that with doing hard workouts in racing flats, and you were doing most of your mileage in fairly minimal shoes. The benefits include stronger and more flexible feet and ankles; more, not less, stability (because you’re closer to the ground rather than feeling suspended above it); encouragement of a lighter, quicker turnover; and simply enjoying running more because of a greater feel of the surface you’re moving over.