Regarding the importance of fiber, I'm certainly not one to go with the general "medical" advice of nutrition (mostly because they seem to have it upsidedown).

But I don't think the ONLY value in fiber is "regularity", if you will. (which is the assumption being made by all the above posts)

I have a good respect for Dr. Scott Connelly's work as well (and I can't wait until getting to the gym regularly is PLAUSIBLE for me...I've tried twice and failed). It was from his "opinions" or "in-house evidence" (as opposed to research evidence?) about fiber that I still struggle to get a decent amount of fiber into my diet.

I'll quote from his book, "Body Rx", about his perspective of fiber. I don't think it can be completely discounted as being pure fluff. And since I don't think there IS much research behind it, maybe the "amounts" can be adjusted up/down from what is recommended. But I'll quote regarding the value of fiber:

"You may say, 'So what. I just read about a study that showed that eating fiber doesn't prevent colon cancer. Why should I eat fiber?' The answer is simple: Fiber burns fat. And protein and fiber together is the most powerful fat-burning food combination there is."

"Good carbohydrates such as fruits and vegetables are a great source of fiber, but most of us don't eat enough of them. (Many of us don't eat any.) I don't want to sound like your mom. So I'll put it this way: Eat your fruits and vegetables if you want to look better naked."
[...]
"In order to produce the energy that runs our body, our metabolic machinery burns glucose. So, you think, the more sugar, the better: I'm giving my body the fuel it craves. But our bodies did not evolve in a high-sugar environment. A little bit of glucose goes a long way. Too much glucose clogs up the metabolic machinery.
If we don't overwhelm the body with glucose-producing foods, the body turns to other fuel sources. One is fatty acids released by our fat cells. In addition, the body burns short-chain fatty acids made from fiber fermented in your intestinal tract. Notably, the burning of fatty acids from fiber stimulates the release of even more fat from fat cells, causing your rate of fat burning to snowball dramatically. This is the power of fiber, and that's why I want you to eat so much of it."
[...]
"While eating more protein will get you in fat-burning mode, eating more fiber will help keep you there." [...] "Why do we need so much fiber? When fiber is digested, it is fermented in the gut and converted into short-chain fatty acids, which can be burned for fuel. The burning of fatty acids from fiber sends a signal to your fat cells telling them to release fat, which your body uses for fuel."

Now, can I put a scientific study in front of you to prove this? No. Maybe they're out there, but I don't care to look.

What does this mean for me? I try very diligently to get a good amount of fiber in my diet. On Protein Power, it is a challenge, and I don't beat myself up if I don't get as much as Connelly recommends because I'm not (currently) following his plan. But what it does mean for me is that I try very much to eat my 7 to 10 grams of carbs in the form of fruits and vegetables (and a high-fiber tortilla a few times a week) so that I'm maxing out my possibilities. I think that's how it generally worked thousands of years ago.

I don't do it for regularity-sake (coffee in the morning works just fine, no matter how/what I'm eating!).
I do it because
1) If it DOES increase fat-burning, then YEA.
2) If it doesn't increase fat-burning, then I'm still eating more veggies and fruits than I ever did when I was not on PP.
Either way, I win.

My own personal guess is...the lower you keep your carb-intake, the less fiber is needed to achieve the above claims. (a nice scientific experiment waiting to happen!) But I find it hard to believe that our ancesters thousands of years ago did without fiber!