I wouldn't imagine I could predict what will happen with the boarding schools into the future.
However, what I would say, is that private education is a market, like any other market and schools are businesses as well as being charities and providers of education. In the end, regardless of which age schools might prefer to start or end at, the availability and willingness of potential customers to buy the product will determine what is supplied. The market in Lomdon and the south-east is different in that there are more potential customers and a much bigger market, but we know that in many areas, independent schools of all types can struggle to recruit and attract enough paying pupils even now. No doubt niche markets will continue to exist, but when niche markets are shrinking, those that supply the niche market (Prep schools) also have to adapt to survive and probably fewer Preps will go to 13 in another 5 and then 10 years than do now.
We are certainly in a period of change. There has been growth in day provision and a decline in full boarding from UK families. In a competitive London and South-east market, Senior schools are looking to protect their futures in a number of ways; they are merging with and taking over Junior schools to secure part of their senior school intake, they are setting up international franchises abroad, they are starting to move away from what was once a primarily 13+ intake, towards a much greater dependence on 11+, whilst initially trying to keep in with their 13+ feeder Preps. Those day schools which are most popular and sought after seem to increasingly realise their power and that whilst they don't want to totally upset their 13+ feeder preps by abandoning 13+ altogether, don't need to offer too much because they have enough 11+ feeder Preps and state school candidates applying. They want to secure their customers for 7 years instead of just 5 and secure them sooner. And the Preps don't have much control over this, but have to judge each year and into the longer term, if they will have enough children in Yr7 and 8 to make a viable provision and if they can offer enough security and certainty to parents wanting to stay in Prep. And these decisions on the day schools do have knock-on effects to boarding schools to. Yes, there are some very wealthy families who have a history of boarding and who wouldn't consider anything else, but there are also many for whom full boarding fees for three or four children is a stretch too far, plus for many, the idea of full boarding just doesn't appeal. Increasingly, most boarding schools offer flexi boarding, weekly boarding and many have a number of day pupils too - again, the balance is shifting and the direction of travel seems clear for British families. There are regularly threads on MN about families seeking schools which are full boarding with lots of British children.....and not that many can be found, as the schools adapt to the changing market, by offering more boarding options beyond full boarding and fill their places with international students too.
There will always be an elite few schools which are heavily over-subscribed and have no problems in filling their expensive places with those willing and able to pay for full boarding. However, the number that can do that seem to be dwindling and the others turn to widen their offering and find other ways to keep going. Some have already started taking in at 11+ too or have expanded their Preps to become an intake place for 11+, effectively running from 11. No doubt many don't really want to take 11 year olds and the staff might not feel that is their forte, and there might be practical implications for numbers further up the school etc etc, but schools do have to be aware of trends and adapt in order to survive. I guess the ancient schools have always done that in one form or another in order to still be around today, and all of the good ones will constantly be looking to what is going on and what they might need to do to adjust and secure their futures....parents would expect nothing less. Parents need to keep abreast of what is going on too - no-one wants to be caught in a position where systems and procedures and plans which would have worked fine a few years ago, are suddenly out of date and few options remain.