Its probably money. Eton and Harrow, indeed boarding, is a lot more expensive, and London has a number of equally academic day schools.
My DC are in their mid 20s but back then we knew several who included Eton as one of their options. One was rich enough to hold onto to offers at St Pauls till the very last minute before deciding day rather than boarding. (His son then switched at Sixth Form.) We knew at least three who did not get into Westminster so opted for Eton. One who opted for Eton rather than Westminster because of family tradition, though the boy was probably better suited to Westminster. A couple who turned down Westminster in favour of Winchester and Oundle, and one whose sons transferred from Colet (now St Pauls Junior) to Radley. (The first was the boy's choice, the latter two because they liked the roundedness of the schools and family connections. I kept in touch with the last family and the boys did well - sports scholarships to the top US colleges.)
Westminster, as well as its own merits, hit a sweet sport for international parents, who did not have a traditional of boarding but were not sure they would remain in the UK for the duration of their sons' schooling as it offered the scope to switch to first weekly boarding and then to full boarding at sixth form.
Eton dropped it "name down at birth" a long time ago. Harry was an aberration. It was not planned that he went there, but his mother died and they decided to keep the two boys together, and close to Windsor. He had to spend in extra year at prep school and even then it appears he was at the bottom academically, a horrid place to be in any of these schools. Gordonstoun, where Zara went, would have suited him better. That said, Eton's intake appears academically broader than at Westminster/St Pauls. All these schools are seeing Oxbridge numbers drop, though Westminster seems to be holding up slightly better, possibly because they attract some uniquely talented kids. Their own pupils opting for the US, plus international competition for and contextualisation at Oxbridge. I suspect that there may be more Oxbridge or bust at Eton. Even in my DC's day large numbers on their central London raised peers happily trotted off to LSE, UCL or Imperial, perhaps with an eye on the US for post-grad.