These examples aren’t really Veblen goods. A Veblen good is something that is desirable solely because it is expensive. For example, $500 hand cream. No better than $20 hand cream, other than that it gives you the warm fuzzy feeling that you’re the kind of person who makes so much money that you can afford $500 hand cream. Then there’s the ‘conspicuous consumption’ part of it - you want the other beautiful people to see that you’re one of them, so wearing a $10,000 dress has value, simply because it’s worth $10,000. Thorstein Veblen coined the phrase ‘conspicuous consumption’ to describe this.
In the two situations mentioned, the exclusivity has actual value. In the first case, making the club expensive keeps out the kind of people the rich don’t want to associate with. Often, such places are also where the rich and powerful strike business deals, ply favors with their clients, etc. Because the riff-raff is kept out, the club can afford to do things like put in antique furniture, fine leathers on the seating surfaces, etc. Things you can’t do in a more open club because it gets destroyed. It may be elitist snobbery, but at its core there is actual value being offered for the high prices.
In the second case, the high entrance standards are the obvious benefit - by ensuring on the best and brightest and hardest-working can enter, the school can offer harder course material and maintain higher academic standards. That in turn gives the degree more value, which makes people work harder to get in. I see absolutely nothing wrong with this.