As airlines do not have access to each others reservations systems then they needed a way of having an accountable document that showed you had paid to travel which they don't have with E-tickets hence the need for paper tickets.
If you buy a ticket with one airline and use it to travel on another or even when purhcasing multi destination tickets on differant airlines, then you pay the money to one company i.e. airline or travel agency, and when you fly you present the coupon to the airline concerned.
The airline then sends the coupons for each flight off to their revenue accounts department where the coupons are sorted into 'own airline' and 'other airlines' then stored onto microfishe.
The 'other airlines' coupons are then sent off to a clearing centre where they all get sorted out and the clearing centre basically works out how much each airline/travel agency etc has to pay each other for all the flights. As you can imagine this is a mammoth task and from what I understand the airlines are actually about 3 years behind with actually collecting the revenue from those tickets.
The revenue from tickets purchased directly from the same airline stays with that airline so that is why they can give you an e-ticket as it doesn't need to go off to clearing as they already have your payment.
Thats why it is always so important that the airline has the coupon before you travel as it works like a cheque in that the airline cannot collect the revenue on that ticket without presenting the coupon first. So look after those flight coupons !!!.
We regularly have to make people buy new tickets when they have lost their flight coupons after they have checked in or if we didn't then they would be in effect flying for free from the airlines point of view, even though they had bought a ticket from somewhere - the airline can't get the money without it.
Hope that made sense - maybe someone can elaborate more or explain it better.
"She Rolls, 45 knots, 90, 135, nose comes up to 20 degrees, she's airborne - She flies, Concorde Flies"