it's all very alarmist, last time I checked, Wetherby and Pembridge Hall are pretty much full. As far as I know, it was about 14 girls from PHS who switched to Bute last year, not 20. It was an unusually high number, maybe it means the teaching and level of abilities at PHS is quite good!! I am sure they have filled the places with other children moving to London in the meantime, so I doubt there was a big dent. PHS is large, they have 60 children per year group, so you'll always have a bit of turnover, especially in such an international part of London.
Some parents are very keen on sending their children to "the best" school in London, and they will always look to switch to an even better school, even if their child is perfectly happy where they are and doing quite well. Just look at the thread "NLCS vs SPGS" on the other forum. You have people whose children are doing great at NLCS, which is the "second best" girls' school in the country, and they will put a lot of energy into getting their daughter into SPGS at 11+, because they think it is "even better" because it is number 1. It doesn't mean that NLCS is struggling or suffering from it, you will just always have parents who want to get the best deal, especially in schools where you find a high share of wealthy, ambitious families.
I agree that one should be cautious about schools that put profits first, and I would generally prefer charitable or family owned schools, but there are less and less of these in London. I still think it is slightly exaggerated to think that Alpha Plus is struggling, it is called long - term investment, of course if you expand and set up new schools, you need to invest money, and you expect it to pay back over a 5 or 10 year horizon, not the following year. There was certainly demand for Wetherby and Chepstow House expansion, there is lots of demand for Wetherby Senior and Wetherby Prep, so I don't think this is the group of schools one should feel too worried about!