I like hiking, and enjoy challenging myself. Sometimes I shoot for my longest distance ever, sometimes I shoot for more technicality, sometimes it's just raw elevation gain over a shorter distance, sometimes it's all of them. I rarely shoot for time, my constraint at that level is typically getting the thing done without having to camp out for the night, but I could just as well do that. I often shoot for time over elevation and distance with road cycling though.
One of the other side benefits of training for speed is that there is just no feeling like finding yourself getting faster with less and less effort. My favorite runners highs have come from taking on a hill that used to be hard, and running it both faster and with less perceived effort than previously.