Going back to your first question – I would say that budget hotels need to partnership with a range of airlines. Just because someone travels in Club World on BA does not mean they would not consider or do use Ibis. Equally someone who travel Ryanair may not want Ibis but perhaps Holiday Inn.
There also has to benefits in the partnership for the customer. Seamless booking and easy ways to gain miles and tier points either with the airline or hotel. In other words the customer wins in price and benefits/loyalty.
Going on to your other point, the idea of giving vouchers is fine in principle, the only problem is that unless they are exchangeable for face value on any accomodation rates they can cause resentment.
Hope that helps and good luck with your coursework