Seems like you're confusing turn rate with turn radius. Or you're forgetting that while it may take the E-D 15 seconds for a full about, that's about 14.5 seconds in the very wrong direction, and 0.5 seconds in a slightly wrong trajectory (little margin for error at relativistic and superluminal speeds).
No, there's not. Just think it through, slowly and carefully.
1) Impulse turn is a maneuver wherein the ship at first points in the wrong direction by D degrees, then turns D degrees, then goes to warp. The ship is at warp, at starting point X, after time T1. This time T1 is
solely dependent on how long it takes the ship to turn D degrees. The turn might take place at pinpoint, or involve a short curving trajectory as often seen, and the results would be the same.
2) Warp turn is a maneuver wherein the ship at first points in the wrong direction by D degrees, then goes to warp, then turns D degrees. The ship is at warp, at starting point X, at time zero. It then moves in the wrong direction for the first second, turns a little, moves in a slightly less wrong direction for the second second, turns a little more, and so forth, until it is moving in the right direction. This has taken the ship the amount of time T2, equal to the time for turning D degrees at warp, and not a second more. During that time, the ship has been heading away from the target for a while, then again towards the target for a while,
but that's irrelevant because at the end of time T2 she is necessarily back at starting point X or at slightly different point X' that is still equidistant from the intended destination. "Little margin for error" is utter bullshit - the universe doesn't care if a ship embarking on a journey of a dozen lightyears starts that journey from X' rather than X. At warp, margins for error are lightmonths wide.
No extra time
at all has been spent during the loop made at warp. A few insignificant lightseconds of distance have been covered back and forth, but nothing has been lost by doing so.
Now, T1=T2 if the ship's turning rate is the same at impulse and warp. Turning radius does not feature in here in any manner. If the ship is more agile at warp than at impulse, then T2<T1 and a smart skipper ought to go to warp first and only turn afterwards. If the ship is clumsier at warp, then T2>T1 and the turn should be made at impulse (unless it is otherwise good idea to quickly go to warp, say, to avoid enemy fire). And if warp turns are more stressful than impulse turns, then it would be a good idea generally to do an impulse turn even if T2<<T1... But probably still a good idea to do a warp turn if one is in a real hurry.
Reason 2, As a matter of conservation, the initial heading would be achieved at impulse, because warp or not, an object in space is always in a ballistic trajectory.
That makes no sense. Why would warp make a difference to ballistics here?
And starships can ignore ballistics. Like, totally. So what if they are on a trajectory that plunges them into the core of a gas giant in a few moments? The helmsman only need press a button and the ship suddenly is on a trajectory that docks it with the local space station. The ship could make a basically infinite number of such course corrections before the fuel gauge needle as much as stirred, or other such considerations arose.
Starships are not spacecraft in the sense Apollo was. They don't have to consider ballistics. They have thrust to spare: if they wanted, they could e.g. travel from Cape Canaveral to Tranquility Base in an absolutely direct beeline, and probably would because that's simpler than doing ballistics calculations. Starships don't make "engine burns" and then coast to target: their engines run hot all the time, apparently constantly accelerating them, and Newton's voice is but a hoarse whisper in the background. The navigational computer only takes it into account as the third term in the error function, for the final but unnecessary hundredth of a percent of accuracy.
Timo Saloniemi