DH was raised CofE and I was raised Catholic, both of us were Baptised as babies and had one male and one female Godparent each.
This would never happen these days, or there’d at least be some ‘sad-face’ photos in the Daily Fail…
However, in 1986, at my Roman Catholic Primary school, in my Year 1 class of 23 children, I was the only child of divorced parents, so was banned from attending weekly Holy Communion classes and had to sit alone for an hour each week whilst my classmates prepared to make theirs. Other children in the class had unmarried parents or had never known their father etc. and could participate, but because my parents had gone through the process of legally ending their marriage, I was not allowed. I remember feeling very upset and left out at the time (I was 6).
This led to me being very angry at the RC Church, but eventually returning to Christianity through my local CofE church in my mid 20’s. Happily, by the time my DSis was in Yr 1, the school had a new Priest and there was a new, more progressive Canon with a bit of common sense in the Diocese, who reasoned that a child should not be turned away by the church due to the actions of their parents.
For our eldest DD, we chose my closest friend here in the UK & DH's best friend and DD2 has my best friend who has since emigrated to Australia (but writes/emails/video chats with us regularly and makes a real effort to maintain their bond) and DH's step-father, who is not particularly 'good with children', but he has a God Daughter (aged 30ish) with whom he has a great relationship so we hoped that this position might help him to form a similar bond with DD2, but alas - he still hides in his study whenever children visit!
Our main criteria were that they are a "good" person; someone we wanted our children to look up to, to feel comfortable to go to with questions and who would offer decent advice (hopefully similar to ours!), if asked. They didn’t have to be Christian and regular churchgoers. It was important to us that they had a Faith, but it wouldn't have mattered which religion they followed.
I don't think it's particularly 'unusual' to have no Godparents these days, I just think that less parents seem to regularly worship and they therefore feel that having a child Christened would be a bit "odd", or they choose to let the child decide once they are old enough to make an informed choice themselves.
I'll admit I do find it a bit strange when parents who are Atheists arrange a Christening for their DC - why go to the effort of having a special ceremony when you don't believe it's real? It's a grown up's version of playing make believe, but in front of all your friends and family whilst choosing two of them to promise things that you don't really want them to do, to someone you don't believe exists!
I think Christenings are getting rarer, therefore a child not having Godparents is becoming more unusual, but I wouldn't call it 'unusual' in itself.