Just wanted to add we also had no trouble gate-checking our stroller with Southwest. Got a tag right at the gate, left it right outside the plane and on the way down and homw when we got off it was right there waiting for us. Once it was even opened up and ready for my DD! FYI--We did not use a stroller bag and we had no damage done to our stroller. It was insanely easy and so helpful to gate check it!
PLEASE, though...anyone gate checking...do it BEFORE getting ready to board. We had a family who, after the third announcement to make sure you had a gate-check tag for your stroller, STILL didn't get a tag. when came time to board, they weren't ready, and they had the nerve to insist the rest of us passengers wait to board until after they get their gate-check tag.

The guy at the gate almost bust out laughing

and let us all get right on while the couple got their tag. Guess they should have been paying attention.