There is a program called Easy strength by Dan John and Pavel Tsatsouline that have you doing each exercise 2 sets x 5 repetitions 5 days a week.
The important part here is to go really easy on each set (hence the name) in order to not accumulate much fatigue.
This program probably works slightly better than a 3 sets x 5 repetitions 3 days a week program. The reason is probably that frequent practice causes more of some not yet understood neural adaptation.
For most people training 3 x a week is more practical than 5 x a week.
However for some people such as firefighters, police officers and military personell, high frequency training may be better.
The reason is that with this style of training you are never really badly fatigued in case you eg have to run after a criminal. The same thing may be harder to do the day after 3 or 5 sets of 5 reps almost to failure squats.
Also there is a other model of stimulus and recovery named the fitness-fatigue model:
In this model you are getting stronger from immediately after your workout.
However the increase in fitness is masked by fatigue so that the performance is worse until you have recovered from the fatigue.
From the link above:
"Without the fitness-fatigue model, we could easily fall into the trap of believing that the fitness adaptations to a workout only occur after a couple of days, because of the reduction in performance. In fact, adaptations probably occur very soon after the workout itself.
For example, in strength-trained lifters, a large proportion of the adaptations in the central nervous system after a strength training workout occur on the same day as the workout. Also, muscle growth is stimulated by a transitory increase in the rate of muscle protein synthesis that is already falling before 24 hours have passed."
This tells us that the fitness-fatigue model is slightly more correct but still a gross oversimplification.
I think both super-compensation and fitness-fatigue are just conceptual models made to fit what has been observed in practice.
From what I understand Yakovlevs experiments were on glucose concentration in muscle cells. The jump from supercompensation of glucose to a general theory of training and recovery is so big that I would say that neither model really have any experimental basis or mechanism behind it.
In practice I think the super-compensation model is generally more useful. It visually illustrates what an athlete must know: you must allow for sufficient time to recover after training. On the other hand you must repeat training sufficiently soon before the super-compensation fades.