BA - Yes, it's true, at 54 myself I would prefer a guy whose kids are grown (my three are in college). In fact, that was a nice thing about the boyfriend I did have - his kids were 30 and 32 and they liked me very much (I am still good friends with them.)
I would consider a guy with teenagers (both because I like teens and I know they'll be gone in a few years) but I am surprised by how many men my age have little children. I like kids but I'm really not interested in getting back into that parenting mode right now. (My best friend, who is two years younger but has a 9 year old, has the opposite problem).
I wouldn't feel put out by women who don't feel the "spark". It is a numbers game, meeting someone online is very artificial, I expect to meet many men before I encounter that same "spark" that I had with the ex-boyfriend. But it is a real thing and worth waiting for.
Yes I'll admit I am looking for a man that I find attractive. But my definition of attractive would not be the same as another woman's. I like tall men - my best friend thinks they are "too tall". I like men with strong noses - even very large ones - and am not attracted to Brad-Pitt-type pretty boys. I don't mind gray hair, just Santa Claus gray beards on chubby faces. And self-confidence looks good on everyone.