Schools select students by academic performance. Pushy parents choose highly academic schools. The higher the rank of the school, the more competitive the type of parent vibe. Sometimes they forge a culture of doing whatever it takes to win.
My SIL’s DC is in a top West London private school with a high number of Ivy League and Oxbridge offers every year. She is telling me about last year, how many parents were not happy with their three-star predicted grade instead of four, and had to hire additional tutors to help them push further. How many parents were not satisfied with their non-Ivy League or Oxbridge offers because their entrance exam (BMAT, etc.) score was not in the top 10 percentiles, so they needed more tutoring and an extra year to polish their application profile with the hope of reapplying in the next year cycle. This adds more pressure on the students in the year below. The school can do very little or has no incentive to influence these parents, and the extra A-star or Oxbridge offer will add to the school’s result tally, which attracts the next batch of pushy parents to join.