Only one person on that thread mentioned that they would try to reduce carbs and then eventually cut them out altogether. This was a newbie, who will probably find his own personal healthy carb limit as he reduces them.
No-one else mentioned 'no carb plans'. One person said it was impossible to cut carbs out completely because even lettuce has some carbs. At least 2 of us said we ate veg as our fibre and carbs.
You can avoid constipation by eating green veg, cauli etc. Drink lots of water and maybe have psyllium husks if necessary. I occasionally use the capsules.
I found constipation was much more of a problem on a low fat diet. Many of us replace the carbs with fat.
A quote from your link:-
"However, if you really follow a low-carb diet correctly, you will be replacing those starchy foods with low-carb, high-fibre vegetables -- which should help counter the constipation by providing as much, if not more fibre, than you had before," says Sondike.
Doctors say that eating up to five servings of low-carb vegetables daily -- foods such as broccoli, cauliflower, and lettuce -- can keep your bowels healthy without interfering with weight loss."