Yeah, I was especially thinking of
The Menagerie as you stated,
CorporalCaptain. I get a weird reaction, though, to the shuttle pursuit scene. I always thought - instead of how fast the shuttle is - is why the Enterprise is going so slow?)
Well, in that case, there is the obvious: the Enterprise is going so slow in order that Spock can be caught. The charade of the trial has to take up as much time as possible, after all, and dragging out his arrest doesn't hurt.
Even if we suppose that shuttlecraft lack warp drive, though, we have got some scraps of dialogue suggesting faster-than-light travel on impulse. Yes, those were probably editing mistakes, but after all, why not take the more interesting supposition that if you really applied impulse power to its fullest, you might achieve as much as warp six?