I hate to argue with the great god Wikipedia but I think this:
"Traditionally, godparents were informally responsible for ensuring the child's religious education was carried out, and for caring for the child should it be orphaned."
is balls.
Godparents are traditionally formally responsible for the ensuring the child's religious education is carried out. That's what they are for. The person who cares for a child should it be orphaned is a guardian, not the godparents, although sometimes they may be the same person, it is not, nor has it ever been, a given that a godparent will take over the upbringing of a child.
Re - the role of the Godparent, OP. You say you did not expect gifts . . . and that you are not religious so you did not expect them to have any religious input into your children's development. So is the job just, um, worship of and attention to your DCs?
What is it that you think the Godparents are actually getting from being Godparents to your children? I mean, what's in it for them? (For example: religious Godparents think that religion is important and see a godparent role as their duty, so that's what's in it for them - fulfilling an aspect of their Christian Duty, dull as this sounds and often is.)
Do you think your Godparents will mind being "sacked" from what appears to be a meaningless role to all concerned?
I am starting to think this is the most pointless thread I have ever read on here.
"I have asked some people to do something pointless that I don't believe in and think unnecessary. They agreed and have done nothing. I am annoyed that they have done nothing although there is nothing I want them to do. Am I therefore being unreasonable to tell them to do nothing with no title, rather than letting them continue to do nothing while revelling in the title of Godparents?"
< boggles >
< goes to find something useful to do >