This is an interesting statement.
In the past, pricing strategies have been such that airlines wanted to sell as many seats as possible at the maximum total revenue. Costs are mostly fixed, so a every single passenger to that flight adds to the profit of it. Or in other terms, the marginal cost for adding "the last" passenger is very low, so even one additional cheap ticket sales is going to add to your profit. Marginal revenue is higher than marginal cost.
Yes, the yield may go down if you sell more cheap tickets, but your profit will go up.

So when I hear this argument, that airlines don't want passengers who book cheap tickets, I wonder what profit maximizing style is at heart. How can profit be maximized if the airline decides they don't want to sell cheap tickets? Of course, if all flights are sold out with tickets in the most expensive buckets there is no need to offer lower pricepoints, so maybe that is the case and the current pricing and profit strategy?