It introduces more factors to consider. One, the kids will be involved in the relationship, so that's more people that have to get along well. Two, they take up time, energy, and resources that could otherwise go to the relationship. Three, the parents are more anchored to their current life, so things like going on vacation or moving become much more complex and expensive. Four, the person will almost certainly have to maintain a relationship with their ex/other parent of the children. Five, if you yourself want to have kids, they may not be willing to do so anymore.
I acknowledge that having kids has its benefits too though. It's not all bad.
I wouldn't mind doing it, but I would have to know the partner really well and feel confident that it would be a stable relationship. I remember having a hard time as a kid when I lost my aunt because her and my uncle had a nasty divorce where she went no contact.
Pros of dating a parent:
You can see how they treat those that are vulnerable and dependent on them
They're typically more stable, conscientious, and responsible
Good parents know that they have to model healthy behavior, so they practice those
You already know what you are getting with the kids, so it's not a surprise
The kids inadvertently tell on the parent if the parent is misrepresenting themselves up front
Can do family activities that would normally be considered odd for only adults to partake
The many benefits of being a parent
If there's shared custody, you regularly get time off from being a parent
Getting older, with an established career makes spontaneity harder as it is. Add kids to the mix and it's pretty much impossible.
I ... don't want that. I like making last minutes plans, 1-2 week long trips, etc. The most limiting factor for me is dropping off my cat at one of my many friends/family members that can watch it (and I reciprocate with their pets).
If I'm going to date it's going to be with someone with a compatible lifestyle.
Not OP, but I was sterilized in my mid 20s. Not only am I not interested in having kids, but I would not be a good parent. I have still dated people with kids who made it clear there would never be an expectation that I become a parent or interact with their kids, which does address those issues, but there are others. Understandably their kids take priority over basically everything except for maybe the factors that effect their ability to provide for their kids (or at least I think they should). That often means they don't have nearly as much time to hang out and build a connection, nor are they able to be as free to do other things due to constraints on their time, finances, or both like going on fun trips. Another factor I have run into that is that usually the reason someone is single and has kids due to entirely positive reasons, and there is often at least some amount of trauma in their past that is often not entirely behind them.
To be clear the above is in no way an absolute and are merely my anecdotal experience and correlations in the given area I live. It is also always worth keeping in mind that I am in no way perfect myself and that it's possible there is something about me that results in the above being my experience.