I don't have yet a feeling of what the concept of haengma is good for.
There are several possible answers. Here's one. I'll the delete the usual perhaps, maybes, mights and so on. You can flavour the resutling dogmatism to your own taste.
Amateurs, and western amateurs in particular, obsess about the opponent's moves, They want to "punish" this move, want to know what to do about that move. They want to invade the ooponent's area. They don't want to defend their own territory until the last possible moment, and then wonder why it turns out be too late or to cause collateral damage. They want to kill rather than live. Living by killing is the ultimate joy.
There is another way. Haengma. In this tradition, you worry about your own moves. You take the view that if your own moves work together perfectly, you don't have to worry about the opponent. He will either make perfect moves, too, in which case you were never likely to beat him anyway, but at least you'll got a draw. Or he will make bad moves. Since bad moves punish themselves (e.g. by becoming overconcentrated or short of liberties) you will win by having better percentages plays (boring isn't it? Unless you like winning, of course).
In practice you are not likely to be perfect yourself, and there are times when you fall behind and feel obliged to invade. But there is a huge difference between counting then invading to catch up and invading just because you can't stand the opponent having a sizeable territory.
Haengma differs from the usual good shape concept(katachi) that is a perennial favourite with western amateurs until they become disillusioned with it. They become disillusioned because they treat it as a static concept - making pretty shapes such as the table or avoiding bad shapes such as empty triangles. Because suji (flow) has not been covered well in English, they have not added this dynamic element. Haengma is really just katachi + suji. But it comes from a one-stop shop, and so is more attractive to some for that reason. But the presentations of haengma in English seem, on the whole, to be rather fuzzy, and in particular don't identify the two components of shape and flow all that well. They seem to concentrate on the flow aspect, which is possibly because of awareness of the underlying meaning of haeng (moving).
If you want to learn haengma, what you are being taught is "how do I think about developing my stones?" This is fairly advanced.
If you have learned just katachi in the past, you have been taught "how do I make efficient shapes?" You have only learned the most trivial aspect. To make it really useful you need to add suji or go on to a full course of haengma.
If, however, you have trouble with the way hanegma is presented, you may find it useful to break it down and learn katachi and suji separately. Learn first how to make efficient shapes and then learn how to develop them. When you can put the two together, a pro will tell you you've got good haengma or good suji. But you'll know that anyway because you'll find go an awful lot easier.
Specifically, good haengma gives you groups that are robust and safe, that can't be bullied, that are flexible, that can move into other areas easily, that occupy or influence space (i.e. potential territory).
It may sound odd, but I've found that one of the best laboratories for observing haengma is games by Japanese women in fast tournaments. Because of the short time limits they rely heavily on haengma instead of reading. But for the same reason they make mistakes, and you can observe the results. They are strong enough to play good haengma/suji most of the time but not quite strong enough to play in a more free-for-all way. Japanese writers often refer to games by female pros as full of fighting - I don't think that's true as the intent to fight is not really there. I think what they are witnessing is what I have just described - a haengma contest.
PS I was talking to T Mark today about the question of telling pro play from amateur play, which he's good at, on the basis of haengma. I told him I had already mentioned the 3-D aspect of shapes which is stronger in pro play (I believe). He agreed but put more emphasis on what he called "sequences". Pros play complete sequences, amateurs don't. I'm sure he is just stressing the flow/development aspect of suji/haengma, which is natural for a strong player. (I have asked him to consider posting his own views BTW.)
The way you said it makes it sound like you think haengma and hiraki are different subjects.