This is part of the issue for me. I know I'm vulnerable because of traumatic experiences.
I would not ever consider a blended family as research shows that in almost all cases it impacts the children very negatively. I would not consider living with anybody while my children live here still (both are in early primary school) for the same reasons. They have been through a lot with family separation and this is their home as much as mine. I wouldn't let them invite someone else to move in so why should they have to put up with that! I'd also never entangle finances again and risk my children's security, or my own.
Perhaps it would be possible to meet a divorced Dad who would want a similar setup: keeping family lives totally separate. But most people in my social circles have not reached first divorce stage yet (I am under 40 and the only single parent of a child in both DCs' classes, for example - not that I'd consider dating the parent of a child in either one's class obviously even if they were single!!! But just that people are all still coupled up mostly).
A man my age who has no children would be highly unlikely to understand that I have limited time to see anybody, particularly as I am a lone parent so any dates involve a babysitter and no man would be coming to my house with my children here, even if they are asleep. If a man with no children wanted children, that's a no from me. Not having any more, I am focusing on the ones I have. If they didn't want children they'd be even less likely to understand the above and also somebody I would probably have little in common with as family life is everything to me.
So thinking about the situations of other potential partners and what would work, it is going to limit a single mother's dating pool significantly. That's not to say it's impossible.
Fortunately all of this is immaterial in my case as I have no desire for a relationship. I am too busy and also love being single and my own company. But of course, not everybody feels like that. And one day I may feel differently, when my children are much, much older and less vulnerable (and demanding!). If I really wanted to date I could, but would keep it entirely separate to my children's lives and be very careful about weeding out anybody unsuitable. It would have to be somebody met by chance or through mutual friends, not through OLD.
And I am certain that - while in the future I may want a relationship again - I will never live with someone again. So much nicer to have your own space and home and see someone only when you want to, and keep a relationship fun and only about enjoying time together, not domestic drudgery and petty stuff about housework and people being annoying. And taking up half of your bed!! No thanks. 🤣
That would also mean that you don't end up in the awful situations I read about here so much, where life is miserable/ someone is unpleasant/ lazy/ horrible/ the relationship has just run its course but you're stuck living with them because of financial entanglements or whatever. It would mean that when it stops making you happy, you can end it. No having to worry about losing your home etc. I don't get the attraction of living with another adult again, at all.