Buoyancy, trim, kicking and breathing are all connected together. If one of these 4 factors gets out of control, it will adversely affect all the others.
And yes, only experience and training (and possibly a good instructors) can improve all of them.
What is wrong is to focus only on one or two of the 4 factors. For example trying to have a deep control of breathing without reducing the effort caused by improper buoyancy and trim or inefficient kicking is not going to work. Similarly, without proper breathing control the buoyancy will always be out of control, particularly for people with large lungs, which cause extreme buoyancy variations.
What I am particularly sensitive to is the interaction between kicking, buoyancy and trim, as the Chairman explained here above.
In many didactic approaches, buoyancy and trim control are practised with very minimal kicking, in static or quasi-static conditions. The student is trained to stay still in water, almost horizontal (but not really horizontal as he looks forward), with arms partially stretched forward in a poorly hydrodynamic position, with legs flexed (knees at 90°) and fins well above the body. Something like this:
While this works well if the diver is still, or moving very slowly, the buoyancy and trim will be severely affected when there is the requirement of moving fast, kicking vigorously. If the thrust given by kicking is not aligned with the direction when one has to move, the diver will need to counteract the positive or negative thrust by changing the BCD buoyancy. The arms stretched at 45° will work as the spoiler of a Formula-1 car, making the head to go down when you are moving fast.
The result will be to waste a lot of energy in counter-opposed thrusts. Add to this that most people are not equipped of proper fins (proper for their legs, everyone needs different fins), and are not trained to using them properly (How many fin-swimming instructors are here? Have you ever made a fin-swimming course?).
This results in another amount of energy wasted in inefficient propulsion.
All this energy requires to be created by burning glucose in your muscles, this requires oxygen and produces CO2, and the latter stimulates a lot of breathing, hence SAC explodes...
And without breathing control, the high CO2 will stimulate short breathing, or even dyspnea, which again is inefficient, not removing well CO2 from your blood, albeit wasting a lot of air. You need well controlled deep breathing, with an asymmetrical cycle, for maximum CO2 elimination.
It is all connected, as said! But for learning proper DYNAMIC buoyancy and trim, current didactic approaches are of poor value, as they are STATIC.
A good freediving course, instead, is where you probably can find good training about dynamic control of your body, learning how to move quickly and efficiently, minimizing CO2 production and hence the need of breathing. Here you see the proper dynamic trim of a good freediver swimming horizontally. Compare this with the photo above and you learn how static trim has little to do with proper dynamic trim: