Lots of clubs give "some" scholarship money that is subsidized by the full paying families. How much they can give away varies by clubs, then some also have extra fund raising events or hold profitable tournaments. A lot of times though it's only for the fees, not travel. If scholarship families can't travel then they need to be comfortable sending their kids off with other families.
It's similar to college - getting the tuition waived still leaves you with the bigger expenses (room, board, books, fees). Club soccer scholarships that only cover fees still leaves you with the most expensive costs (travel, meals, family travel etc.) on the higher leagues.
Comment