The point of having a bond with the Godchild is to make them feel special. Here comes a holiday when you give gifts to people to make them feel special, and you choose not to because you feel bad about not buying for kids who are NOT your Godchildren. Well the whole point is to bond with your Godchild! You were chosen to represent that child, not the whole family!
Just a tad catty on your assumption though, don't you think? But no, I LOOOOOOOVED my godmother! She was the best. She had all sons, and I had all brothers, so for her, it was a chance to do girly things. She would paint my toes, and have special sleepovers with me. We'd watch girly movies and talk on the phone.
And no, it was my one brother who had crappy godparents. Everyone would open their gifts from their godparents and my brother was always left out. Even when my parents would take us shopping to pick out a present for our godparents, my brother would get his hopes up every year that perhaps this year would be the year his Godparents remembered him, but nope. He got very self-centered Godparents that weren't into spending time or even $5 on their godchild. We all felt bad for him, really. Mine was broke as hell, but I knew I was loved and that I held a special place in her heart. Her gifts were never big $50 gifts. Often it was under $5, but it was something that my mother would never get me. Nail polish, lip gloss, hair scrunchies (which were in style then), sometimes cute winter boots, etc. She was so much fun. Sadly she died when I was 18, but I am so thankful for that bond, and I would give anything to have her back and ask for advice with my own kids and just sit and snuggle with her.
I hope your Godchild isn't the one waking up on Christmas wondering why you didn't get them anything when the other kids are all opening gifts from their Godparents. It seems to me you're passing up the opportunity to form that special bond. But hey, you feel bad, so go with that.