"I think the assumption that if you don't have a relationship your life is so much about your children that you'd grow old and bitter is a weird one."
Surely it depends on whether you want to be alone? If you are lonely, and want to have a new relationship, but feel you can't, because you have children, this could lead to you becoming bitter. Of course, if you are happy to stay single, and to raise your child as a single parent, you are likely to be happy about your choice.
"But STG it is a bit different, as in most cases you wouldn't move your friends and hobbies into the home and so on."
Well - it does depend on the hobby, of course. My DC would tell you that my yarn stash and my book collection are, between them, taking over the house!
But to be serious, what I was saying is that it is perfectly possible to have the early stages of a relationship without the children even knowing, let alone having their lives affected at all - and of course you shouldn't introduce a new partner into your children's lives until you are sure that the relationship is a long term one. But it is perfectly possible to build a relationship with a new partner, introduce them gradually and sensitively into your children's life, and, in the long term, build a new family that can be a truly positive, good thing for your children.