Unless you charge a LOT on those airline credit cards & fly a lot with that airline, the miles you get aren't really worth the hassle. You get a free ticket or something similar when you first join, but basically they just want you to have their credit card to make the fees from things you purchase. I have had some of those credit cards in the past and you may not accumulate enough miles for a ticket or upgrade before they expire. If you live in a hub city and mostly fly on one airline, it can be a good deal if you charge enough. However, airlines often merge or relocate hub cities and then the benefit isn't nearly as good as it first seemed.
Having credit cards from multiple airlines is less likely to be of benefit.