Yes Alex their view of too higher risks absolutely correct. In a previous life long ago I used to work for Barclays & we carefully vetted companies wanting to accept credit cards, starting off with a low floor limit (the maximum they can take on a card) & increasing as they proved their financial stability. Even car showrooms rarely let you pay more than the deposit with a CC as you say with 2%+ handling charges that eats into their margins. So for something as risky as flight training CC companies are going to edge on the side of caution.
Remember banks only willing to lend money when you don't need it & only too quick to call it in when you do. Even more reason to support your PAYG or no more than £5k up front if I remember correctly.