Building strength is CRUCIAL in MA.
There is just no way around it and at every level, strength is needed.
And not just in MA, in every day life.
Not a day goes by that we don't have to lift or push or pull something.
Strength is vital and indespensible.

There is only ONE way to build strength and that is to progressive resistence.
In short, we get stronger by making our muscles stronger and they get stronger by having to do more ( exert muscular force) than they are used to.
Progressive Resistence means just that.
NO ONE disputes that.
What IS disputed at times is the means to create that resistence.

There are only TWO ways to create resistence for the muscles to get stronger and that is:
With "weight": Stone, wood, metal, body, any object that is heavy.
Without weights: this is when muscular tension is used to "activate" the strength building response and it typically and commonly called "tension" and it can be isometric ( not moving) or iso-kinetic ( moving tension).

Both ways have merits and both was have cons.

The pros of using a weight is obvious:
Resistence can be measured and different levels of intensity can be used.
Progression can be measured.
The cons are minimal:
There can be a danger to using weight that is heavier then we can handle.
The availibility of training space and equipment.

The pros of "no weights":
No need of equipment and can be done anywhere.
No danger that comes with using equipment.
The cons are numerous though:
No way to measure intensity besides 100% ( you can tell if you are exerting 50% or 80% only if you are tensing 100% or not).
No way to measure progression.
No "unbias" way to measure intensity.
Isometric tension mainly develops strength on a static pathway.
etc.

While some can state that the "bulking" up of muscles is also a "con", they tend to not realize that the EXCESSIVE bulking is based on diet and not so much the Strength building protocol one is following.
They also tend to not realize that there are strength building protocols that focus on "pure strength" only and that do not "induce" muscle growth.

The "too bulky" argument is a false one because it is based solely on the "bodybuilder" view of STrength building.
People that comment that weight training makes on "bulky and slow" seem to ignore the muscular builds of sprinters, track athletes, american football players and the vast majority of pro athletes.

In short, to build strength for ANY physical activity ( athletic or otherwise) we must do it via progressive resistence training and that training can be done wither with "weights" ( barbells, dumbells, keetlebells, stones, own bodyweight, etc) or with "muscular tension" that is done either with no movement ( isometric) or through a given range of movement ( iso-kinetic).