The Crown Estate isn’t owned by the Royals. It is part of the government, profits go to the government. It manages the Crown lands which the royals handed over in return for a regular income (the civil list).
The Look Out and, I assume the car park, are leased by Bracknell Forest Borough Council. I guess if car park fees were levied they would go to the council, not Crown Estates so would have no impact on trail maintenance.