Interesting question. Obviously varies hugely from baby to baby, but for most babies seems to be somewhere between six weeks and four months - as in, plenty of babies stop night feeding at that age and still grow perfectly well.
However, one problem to be aware of is that it's not certain how that impacts on overall milk supply in a breastfeeding mother. Anecdotally, it seems some women will drop their supply if they try to go for a period of several hours without nursing on a regular basis. And there doesn't seem to have been any real research done into how often this happens, or how the odds of it happening are affected by whether you nursed frequently around the clock for the early weeks to get a good supply established, and/or continue nursing frequently during the daytime after cutting out night feeds (both of which would be likely to reduce the risk of losing supply.) So, on current knowledge, all I can say is that if your LO starts STTN at a few weeks or months and you go on nursing frequently during the day, then it is at least theoretically possible that your supply might drop to the point where you have to supplement earlier than you wanted to, and it's not possible to give any sort of clear information about the chances of that happening. I wouldn't flip out over that, but I mention it in case it's something you want to figure into your calculations.
I completely agree that a lot will depend on how easy or difficult your baby is to settle and on how well he or she eats. At the same time, though, I don't think that means you just have to throw your hands in the air, leave it to the will of the gods, and make no effort at all to steer things in a particular direction. It's good to be flexible, but not to the extent of assuming you can't do anything to change things.
I've just been reading Pamela Druckerman's book about French parenting (I've got it under the title 'French Children Don't Throw Food', but I think it's sold as 'Bringing up Bébé' in the States) and found she made some really interesting points, of which one was the chapter on French babies' sleep. What she found was that all the French mothers she knew seemed to have babies who slept through the night in the first few months or sometimes weeks, and to take it for granted that this would be the case, but at the same time none of them seemed to be doing this by leaving the babies to scream - on the contrary, they seemed very put off at the thought of CIO. So she wondered how on earth this was happening. After talking to a sleep expert and to a lot of French mothers, and reading research papers on the issue, she realised the key point was that they didn't swoop straight in to pick their babies up and feed them every time they woke up. Instead, they aimed to observe their babies and figure out whether they were actually hungry, or just surfacing for a minute between sleep cycles and trying to get back to sleep. And all of this was very much framed not in terms of CIO, but of respecting the baby's needs. The way they thought of it, respecting a baby's needs means that you feed him when he's hungry, but also that you don't feed him when he's not hungry. That if what he needs is to be given a couple of minutes to get himself back to sleep, you do that. Or if he needs to be patted and soothed to help him get back to sleep rather than picked up each time, you do that. And the result, for these mothers, was that they had babies who typically slept very well at early ages. (This was also backed up by the research she read.) So, that seems to me to be an important approach to try, once breastfeeding is well established.
As far as the WHO's recommendations go... well, I've read the reasoning they give, and it seems to me to be heavily based on the needs of people in more deprived settings. In many countries, children are at major risk of malnutrition and breastfeeding for two years really can make a difference to their survival rates, and also mothers may have no other way of spacing out the babies and limiting their family size. I haven't been able to find any evidence that it's important to breastfeed through the night if you're in a setting where other food and birth control is easily available. (And I have found some evidence - not enough to be conclusive, but enough to give me pause about the idea of night-feeding a toddler - that night breastfeeding can be associated with tooth decay. So it's not like the decision to avoid prolonged night breastfeeding would be entirely devoid of supporting evidence either.)