That's absurd. You're comparing shoes to bicycles? No, I don't like trail runners ruining the quiet solitude of a walk in the forest, refusing to slow down for hikers, pushing past on narrow trails after yelling "PASSING!" If they want to run, they can run (or bicycle) elsewhere. Both modes of locomotion are antithetical to sightseeing or an appreciation of nature and it's beautiful solitude. Those people aren't naturalists, they are competitive athletes, and their presence is obnoxious. 

I started backpacking in 1973, by crossing the Selway-Bitterroot Wilderness in a glorious, sweaty week. I was the first backpacker the head ranger had heard of. He told me "I wondered when someone was going to do this." Over the next two decades I hiked wildernesses from Colorado to Alaska. By the time I had largely quit, designated wilderness had become relatively crowded. I can imagine how much worse, with jostling and tempers flaring, it would be with "trail runners" and bicycles flying by.