I don't believe it's down to style, it's down to results. To be honest, I personally can't think of a situation I would use it for. I know it's recommended, we have the linked video etc etc but internet advice you have to take with a grain of salt. People on the internet are searching hits and I found looong ago internet advice is often unreliable.

I'll explain the reasons I don't use it.

First, if you are a AF-S user and are looking for accurate focus with the AF-ON button set in AF-C mode, you won't achieve it. You'll miss critical focus in a massive amount of shots.

If you are a AF-C user predominantly, using AF-C works best for me without needing the AF-ON feature. The only difference is AF-ON will give you that "hit/miss" AF-S lock option if your subject is stationary. The technique to achieve AF-S in AF-C is simply frame more loosely "if" required so you can place a focus point on the required target. The AF system will hold the focus quite well on your subject. You are not always "forced" to fumble around changing AF-S/AF-C modes as they try and tell you. The advantage you get without using AF-ON is once the subject does move, the camera will react far more quickly than you realizing, "Hey, it's moving now, I better press and hold the AF-ON button!"

Then there is VR. From memory it doesn't activate till you press the shutter button and very well may not have time to settle before you trip the shutter. Can't even recall if this is accurate to be honest so people need to check this out for their own camera model.

Then there is the comment made by Bill_de. Thumb available to quickly switch focus points is far more important than wasting it on the AF-ON button.

Finally there is AE lock. The AF-ON buttons are perfectly placed to assign AE lock which is a critical feature. This way even if you have a grip, AE lock is always quickly at hand in both camera orientations.

For speed, ease of use and results, I personally have found it is best to not use the AF-ON button for AF.

It's almost too bad this is called 'back button focus.' Maybe alternative focus would be better because it doesn't have to involve your back button at all. Some complain that their thumb gets in the way or something else isn't right. Back button focus can be assigned to any button. Mine is assigned to the two FN buttons on the front of the camera and controlled by my third finger most of the time. (I just had to double check this as it's so automatic for me.) Set your camera up such that it works best for you.
...Cam

Well, it's not on the top, it's not on the front, it's not on the side,
it's on the back. (Thumb works it.)
The back narrows it down, where "alternate" could be anywhere on the camera.
The back button is by default, an alternate button.
Call it what you want, I'll stay with convention.
Unless you are able to change convention, like to AFB.

Maybe they should color code all the buttons (mine are ALL black).
Then I'll nickname my camera M&M.