Pros:
-Accrue points at a good rate for things beside travel, like eating out
-More flexibility on redemptions: transfer points to whichever airline flies where you want to go & has the best prices
-Diversify against risk of mile devaluations, which are all too common with domestic airlines these days
-Depending on the card, you might get nice additional perks like companion fares, travel reimbursements, free hotel nights, lounge access

Cons:
-Harder to achieve FF status with a specific airline, though if you don't fly much that's unlikely anyway
-No free checked bags