[edit]this post turned out as a lot more rambling than it looked like in my head...
I think we are getting confused by definitions and applications of qualities for different activities.
I will side with
@Anna C here, there are generally accepted definitions for the 3 pillars of general human ability (let's leave aside skill, mobility etc for the moment to keep it simple).
- Strength is a quality, and is defined as the ability to exert maximal force against a resistance
- Endurance is a quality, and is usually defined as the ability to sustain a certain effort for an extended period of time
- Speed is a quality, and is usually defined as the ability to produce force rapidly for short amounts of time
What muddies this discussion is the application of these qualities to certain activities, like walking or running.
Here's a picture (linked from cyclingtips.com)
So the 3 qualities are the corner stones of physical ability. All of them are involved to different levels in all physical activities. They also all rely on each other (speed relies on strength and endurance, strength requires speed and endurance, endurance requires strength and speed), on differing levels.
Combining them (admittedly simplified in the triangle view) gives rise to further qualities:
- Strength endurance, sustaining a certain level of strength for a prolonged period of time
- Power, exerting maximum strength quickly over a short period of time
- Speed endurance, exerting a certain level of force quickly over a period of time
Again, all 3 exist on a continuum, and are used to different levels for different activities.
If we go by this we can classify each activity on the main requirement and thus find out what potential it has for achieving a training effect.
This continuum can be applied to all physical activities (powerlifting requires lots of strength but very little endurance or speed; olympic lifts require lots of power hence lots of strength and speed but not much endurance; etc), but as the discussion here is linked to walking we can focus on that.
Walking requires all qualities, but endurance (both speed and strength) is by far the highest requirement. Speed and strength qualities are required at low levels only (but still cannot be neglected).
So, someone who does not have enough strength to walk for longer periods will absolutely build raw strength to be able to display the strength endurance required for his walking. However once that level is reached there is almost no further building of strength involved, but rather that level of strength gets expressed and trained toward the strength endurance quality.
This also means that building strength through proper strength focused modalities is both quicker and more effective to achieve the required level of maximum strength, to be converted into strength endurance.
Running is about the same, but both strength and endurance qualities are required to a higher level to be able to express the higher strength endurance running requires. But still the same principles apply (as they will for all endurance focused activities like biking, swimming, rucking, etc)
So, does walking build strength? Yes! But only up to a point. Once the point of strong enough is reached it will convert raw strength into strength endurance (which is a very useful quality for daily life but still different from how raw strength is defined). Very little strength will be built.
Note that this changes once you change either one of the expressions of the 3 pillars: increased bodyweight means increased application of force against resistance so you need higher strength requirement and training; increase the duration and you need more base strength to maintain the same strength endurance and speed; increase speed and you need more endurance and strength to maintain the same duration; etc)
Does strength training help walking? Yes! Clearly, the stronger you are the more you have to convert into strength endurance (you become more efficient). Again, up to a point, where strength training limits endurance training and becomes counter-productive
Does walking help strength training? Yes, but only to the point of where you have enough strength endurance for your strength training (sets of 1, sets of 5, etc, all have an endurance component, but very little compared to the strength requirement). After that level is reached walking will not help strength development.
Is walking absolutely required as an activity for daily life? Yes! But as a completely different discussion.
If all you care about is strength (like a powerlifter), or power (like a thrower), then it is actually counterproductive, as lots of energy will be shifted towards training the endurance quality, which is not required for and a hindrance to your sports performance.
So, it all depends on goals and performance requirements (which we all knew already)
Still, when discussing different activities, a clear definition of the qualities involved is needed, otherwise we end up all saying the same thing in a different way
