Here was my longer answer on RedUser:
There is a lot of voodoo surrounding soft lighting techniques...
Think of it this way: the softness of a light is determined by its SIZE as a source (the diffusion frame or bounce surface is considered the light source in this case, not the unit lighting that frame of material) relative to the distance to the subject. THAT'S IT.
So if you light a 12' x 12' frame of diffusion material evenly from edge to edge with no variance in intensity throughout, or fill a 12' x12' bounce surface evenly in the same manner, it cannot get any softer as a source unless the subject moves closer to it.
That's all you need to know, it's the size of the soft source that determines its softness. What different different materials do and what doing a book light does is just create variations in how evenly you can fill that diffused area because it is very hard to perfectly fill a diffusion frame from edge to edge. But once you do it, the light cannot get any softer, so adding even more diffusion material isn't going to add more softness unless you are using the soft source to fill an even larger diffusion frame.
I recall a demo that Roger Deakins did at a union lighting seminar where he lit (with 1K's I think) a subject with a semi-circle of 4'x4' bounce cards and then re-lit with 4'x4 diffusion frames with the light passing through the frames. He basically got the same effect either way. His point was to not overthink this issue of bounce versus diffusion frames, a soft light is a soft light -- which technique you choose is partly just a practical issue, i.e. do you have more space behind the material for the light or in front? Also it is easier sometimes to set up flags in front of a diffusion frame rather than a bounce card because you don't have to work around the lighting unit.
So in regards to a Kinoflo, the size of the soft source is the size of the unit, with a 4' 4-bank Kinoflo, it is roughly a 2.5' x 4' soft source. So if you set up a white surface instead of a Kino but bounced a Source-4 Leko into it with the blades pushed in to create a rectangle of light that was 2.5' x 4', it would be similar in softness to the Kino, assuming no hot spot or kick in the surface of the bounce card.
So when asking if a Kino would be just as soft as an HMI bounce if either were passed through a diffusion frame, it depends on the size of the HMI bounce area. Odds are high that it probably would be a bigger area of light on the bounce surface that 2.5' x 4', right? So it would be softer than the 4' 4-bank Kino. But let's say that the bounce area is roughly a 5' diameter circle -- well, two 4' 4-bank Kinos, one over the other to create a wall of 8 tubes that is about 5' x 4' in size, well, that might be similar in softness to the HMI bounce area, at which point the difference will probably be more a matter of intensity depending on how bright the HMI was.
It also depends on how evenly you fill the diffusion frame you are aiming the Kinoflo through versus the HMI bounce. It is conceivable that a single 4' 4-bank Kino could fill a 12'x12' frame of diffusion evenly if backed far enough away, more evenly than an HMI bounce that was much closer to the 12'x12' diffusion frame, in which case the Kinoflo would create the softer effect. But by that logic, a hard 650w tweenie backed far enough away could evenly fill a 12'x12' frame of diffusion and create an equally soft light, assuming a fairly heavy diffusion material.
FYI, Robert Richardson used a giant wall of Kinoflos behind diffusion to create a dim grey ambience on a heavily fogged soundstage to create the opening of "Snow Falling on Cedars" of a boat at night stuck in a fog bank, the softened Kinoflo light basically just glowing the smoke evenly to create a dim separation from the silhouetted foreground elements.
But as for why someone might bounce an HMI and then pass that bounce through a diffusion frame, it might be because he needs the intensity of a bright HMI, maybe he's bouncing a couple of 6K HMI PAR's into a 12'x12' frame and then passing that through a 20'x20' frame of muslin -- it would be hard to get a wall of Kinos to be as bright as some 6K's bounced into a white surface.