Cyclists don't have to worry about independent recovery because the cranks make it automatic, but that doesn't make it any less important. The weaker the hip flexors become, the more of a liability the recovery stroke becomes, and the less efficient the motor.
The hamstrings have a similar relationship, possessing the potential to be a contributing factor in the pedal stroke, but more often than not, they are a liability that places a greater load on our over-worked quads.
Moreover, this whole complex tends to create a progressive anterior pelvic distortion that creates a mechanically inferior leverage posture, and also tends to manifest in progressive injury patterns.
Muscular Teamwork
Whenever possible, you should try to make the recovery musculature work more as contributors to the stroke rather than liabilities. This is not likely to result from just riding lots of miles and following the cranks around in circles.
You must systematically teach the legs to lead the cranks around in an efficient powerful path. The same muscles you feel when you isolate one leg are the same ones you need to strengthen and teach to contribute to the stroke.
The hip flexors and hamstrings need to be able to produce powerful contractions that help the quads exert force on the down stroke and they have the potential to do that, but there must be conscious neuromuscular conditioning to make that happen.
It is easy to forget sometimes that the bike is not a natural appendage that was made to make us better locomotives—in actuality the bike masks our progressive weaknesses. After years of observation, I have seen consistent regression in efficiency in athletes who aren't consciously working towards efficiency improvement.
Play the Tune of Efficiency
A couple of strategies have emerged as givens in my search for mechanical efficiency. First, assess the stroke and get an idea of your efficiency quotient. Get a spin scan done. Find out how balanced your stroke is. Do some isolated pedaling to see how strong your hip flexors and hamstrings are. Be observant of inequities between right and left legs.
In general, most riders will need work on hip flexor and hamstring strength, and will need to develop the specific neuromuscular ability to put that strength to work in a pedal stroke. I recommend a year-round program of isolated leg drills to develop strength and neuromuscular efficiency in these muscles—the musical equivalent of fumbling around with basic chords.
It is also important to obtain your own structural profile and aggressively seek balance—strive for balance fore and aft, starboard and port; strengthen what is weak, lengthen what is short. Proper bike fit is a big factor. Make the hip flexors and hamstrings the prime-movers they were designed to be so that other very powerful muscles like the glutes and erectors can be better employed.
This is not an offseason program. It needs to be an essential element of the daily cyclist's training regimen all year round. For long-time cyclists, there are many old habits to break, and gross imbalances to correct. Get good information, start now, start slow, and progress systematically and patiently.
Like playing a musical instrument well, it takes continuous time, energy, and patience. But in the end, you'll be playing the tune of efficiency, and we should all like the sound of that.