As someone who uses fedex a ton for business I can say that you will save decent money by signing up for a free fedex account. Fedex has done about 3000 packages for me and never lost one. I have stopped paying for insurance because the risk of loss is so low.

I think fedex and UPS don't have airport counters because many people want their bag when they arrive so they would have to ship it overnight. Most people trying to save a few bucks over the airlines will plan in advance and ship before they leave. It will be more cost effective to have a pickup scheduled at your home if you don't want to drop it off. Though I guess whne returning home you would want to use the airport location.