I think there is no right answer, a lot depends.
I agree that a lot of single parents make it hard for their kids with dating, and some I would put it more strongly than that. I babysat a girl in that situation for a while, her father introduced her to one serious partner who he broke up with, he then met and married someone else - I think it was all hard for her though that marriage has been stable.
Her mum however went through a string of partners with their own kids, moved in and out with three or four, and frankly I think it was terrible for the children. And she was in many ways a good mum who loved her kids but had a serious blind spot about that.
On the other hand, my mum remarried after she and my dad divorced, and I think it was very positive for me and my sister overall. It was harder at the beginning and I was not always happy, but it definitely gave us another active parent, a male role model, and more financial and general stability.
The main thing with this though is my mum never introduced us to any men she just dated, and she and my stap-father agreed beforehand that if they did introduce us it would be when they had already settled on marraihge, and there would be no question of it being a trial or experiment - if they married, that was it. And he treated us as his own, including financially - he was just as responsible for making school lunches, taking us to events, and financially (which was actually a big step up for us.) There was no question of us being kids who lived with our mum's husband as a sort of roommate, we functioned as a family.
If I were in that situation, I wouldn't necessarily preclude remarriage, but I would be very picky. And if it wasn't on the cards I might date but I'd not have the kids involved with the person as my boyfriend or anything like that. At best they might know him as a friend.