Some trail shoes are mid height for stronger ankle support. There aren't any high top road shoes. Lacing tightly up past the ankle should reduce stress from impact by increasing the rigidity of the ankle+foot and giving an extra bounce. Because of modern light fibers the weight of the extra material would be negligible. With lace up high tops runners who currently tape their feet could use less tape.
Puma and Nike made high top cross country spikes but the shoes seem to be discontinued. The tops were like built in socks and didn't lace up anyway.