Are you talking about the Clįsic card, which is the base level of Iberia Plus? Or the Iberia Classic, the Visa credit card?

With the credit card you have to use their special link to purchase the ticket, otherwise you don't get the discount. And you're correct, other than the discount and the whopping 1 Avio per 5€ you spend, there is no benefit.

FYI the Classic has been/is being replaced with the Iberia Icon card, which you should absolutely switch to if you use it at all. It gives 1 Avio per 2€, and more importantly you automatically get Iberia Plata status, equivalent to OW Ruby. I mean, it's still the worst airline credit card on the planet but as we say in Spain, es lo que hay.