LO, you are right in that a higher transit speed equated to a faster reaction time but in the case you cited it would only apply to the first aircraft in a patrol cycle. Suffice to say, the case you cited was rarely the case.
A more important factor is reach and endurance. Given equal endurance, say 10 hours, where one aircraft could transit for 2 hrs and be on task for 6,the other might transit for 3 and be on task for 4. You need more airframes and crews in the latter case.
Then take a patrol box 120 across. The Nimrod could dash in about 15 minutes whereas your slower aircraft might take 20-25 minutes. Time late at datum is a critical factor.
Then another need for speed may be less obvious - the need to run in the case of a hostile threat. Running bravely away at 400 kts or more feels much better than running at 200 kts.
Been there, done that. It was not very comfortable sitting a 100 miles off when a fighter was launched against us.