I work in a prep school with boarding. In reality, it's already pretty much as you say - dying out except in exceptional circumstances.
We have just over 300 children in the school. The vast majority of these are day children.
Our flexi boarding programme is very popular. We have between 25 and 75 children boarding each night, depending on the day of the week (Friday is the most popular as we have Saturday school and a night of boarding is cheaper than a baby sitter). For the children who board one night a week it's just a fun sleepover.
We have around 8 children who board 2 or 3 nights a week. These tend to be children who live 45-60 minutes commute from the school and/or their parent/s work very long hours in London. They are often at the school because it meets their learning or social profile rather than it being the closest school.
We have around 10 weekly boarders. About half of these are on full bursaries as part of a programme aimed at providing fully funded boarding education for children from exceptionally chaotic or deprived families. The other half tend to be your traditional, multi generational boarders - or sometimes those who don't get into the very selective day schools in London.
We have around 10 full boarders. These are split between those on the full bursary scheme mentioned above and international boarders. The international boarders are often just here for 1 or 2 terms as an intensive English immersion experience.
All our full, weekly and 2-3 night boarders are Years 6 - 8.
Very few of our 1 night boarders are below Year 5. None are below Year 3.
So, even at a 'traditional boarding prep' actual full boarding for no good reason is very, very rare.
Even 15-20 years ago, the picture across boarding schools was different - there were a lot more who boarded young just because it was family tradition. Those families mostly wait till 13 now.