By employing a warp drive at less than 1000 millicochranes, if we assume the ST warp principle is along the same lines as Miguel Alcubierre's theoretical model. An Alcubierre warp drive is free of time dilation effects at any effective velocity, because time dilation cancels out of the equations when you compare shipboard time to an external observer's time.
I've never liked this explanation--if it's just moving space at less than the speed of light, there isn't much purpose to those giant torchship rockets on the saucer section. Maybe Probert's warbirds do that

And of course, without Alcubierrian magic, they aren't hitting anything like .25c with the propellant load they're capable of carrying in the volume that isn't occupied by people, air, holodecks, and such.
On the other hand, that does make impulse lame and only useful in very limited situations--I'd assume the major ones to be combat and moving out of the ecliptic where the majority of dust, intersystem shipping, and civil transporter beams are. But you don't need tons of speed to move out of the ecliptic in a reasonable timeframe, and even then it's hard to imagine why warp wouldn't be possible going solar north or south, where one would be unlikely to smash into stuff.

*What's the deal with the deuterium fetish Trek has? Especially antideuterium? Why would you make antideuterium? Why would you use it? Do they like electrically neutral antimatter fragments with ten minute decay times launched at near-c through their ships? Maybe I misunderstand annihilation reactions. : /