A comment in this answer about building up stamina for a commute says not to coast, even after intervals.
Why not? How is coasting different from light pedaling with minimal load (which I'm assuming is the alternative for recovery)?
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The reason (and I'm no medical expert) is that it acts as a gradual cool-down period after the hard exercise. During any exercise it is good to cool-down by still moving and exerting less effort. Keeping the muscles moving helps remove lactic acid from the muscles (which contributes to cramping) and keeps the blood flowing. Also sudden changes between hard pedaling and stopping can make your blood pressure change more quickly. It is better to make gradual transitions.
Basically, for all the same reasons that you should cool down for a few minutes after any strenuous exercise. In intervals, you are just doing it over and over. http://en.wikipedia.org/wiki/Cooling_down
From a bit of searching through training sites after reading that comment last night it seems that it is for the same reason that at the end of a 10k run you don't want to stop; if you do your muscles don't get a chance to remove toxins such as lactic acid that have built up.
The guidance for runners is to walk around and stretch gently - I'm guessing that the guidance on not coasting is for exactly the same reason - keep the muscles moving so as to aid in lactic acid dispersion and the removal of toxins built up during the exercise phase.
Yes, as others indicated, it is for the same reason that runners don't just stop and sit down between intervals.
I would add that it is also a matter of form. As much as they are about power, intervals are also about developing good form. If you punctuate them by totally slacking and using the bike as an easy chair that's somewhat counterproductive.
Question is why coast? Personally I made an aim not to coast too much when riding( checked with a cadence histogram chart, usually is around 2~3% of time ). This is possible even after doing all out 30second intervals, I am still able to push out enough power to move me forward at a decent speed.
The benefit of not coasting is obvious, your body will adapt to not getting a relief which in turn will make you a stronger rider. Of course there are times when you are completely cooked, this is usually during long rides, you can coast for a couple of seconds to rest the legs a bit but this is a different scenario then what you are asking here.