The OP stated that his wife doesnt attend group - so without the consultant support she is way more likely to struggle anyway. I am however quite curious as to why the OP wants to diminish her efforts with comments about why the "science" of the whole plan is contraindicative of its success. If it didnt work, then people wouldnt pay to go to class, buy the books, and it wouldnt be a business that has lasted for 40 years. It would have been dismissed as total hogwash in five minutes and they would have gone bankrupt years ago.
Even if the OPs wife is not losing weight effectively and IS following the plan to the letter, which is clearly not the case, as he states that she does it in phases, gets disillusioned, stops, and then goes back on it again, well then it is to be expected that the "net loss" will not be much of anything to speak of, simply because she is not following the plan consistently, and so every time she comes off it, she will rebound.
OP, I reiterate my earlier comment that your wife should attend group, so that she can get the proper support to ensure she is following the plan properly, and that she should test out variations of the plan that dont involve endless carbs, whilst many people get great results from the green plan, others do not and it may be that the one she is following simply does not suit her own personal body make up and metabolic system.
But overall, whether she is losing weight or not, you should bear in mind that whilst following the plan, if she is in fact following it correctly, which we have yet to establish, she is still eating a much healthier diet when ON the plan, than she is likely to be when OFF the plan, and she should be supported for that, and not analysed about the minutae of calorific details. Recent research has started to ask questions about how relevant calorie counting actually is, and that we should perhaps re-evaluate and classify foodstuffs based on their nutritional value instead. Which is, if I had to summarise the SW Plan in a nutshell, effectively what the whole thing is based upon. NOT counting the calories, but eating in the most effective and beneficial way for weight loss without feeling deprived.