Obligations are definitely something to consider. Not just with children (who are obligations generally shared with a partner, and as a result can lead to spending more time with a partner than another) but also parents or other family members who might be sick, or a very demanding job, etc. These can mean you're less available.
I think it's fine to have obligations and doesn't make you "undateable" whether you're single or not. But you need to be pretty clear about what the obligations are from the get go, and to understand that some people might struggle with it, or need more intimacy during the time that you do have time for them.
I think as long as you communicate and try to see things from each other's point of view, things should be fine. An advantage of polyamory is that is you are very busy and cannot see a partner often, you can still have quality time with them when you're available, and when you aren't they might have other partners around. If they're mono or only have you as a partner at the moment, they might feel neglected.
I think obligations can still be perks: children require responsibility and work, BUT generally they also provide joy. Same with other friends or family members, they presumably provided something in your life as well and you're doing your share of giving back. And a job might be demanding, but it feeds you and keeps you healthy.
BUT generally, despite the fact that they usually have perks attached, obligations are still easier to understand, and don't make you an asshole by default.
What I mean is that if you don't take care of your children, or of a dependent adult, they might very well die. If you don't work hard at your job, you'll get fired, lose your source of income and starve. There are real consequences that can lead up to, in the most extreme cases, actual death.
In contrast, if someone says "we are married, therefore in any argument, we will side with each other", they might justify it as "protecting their marriage" and imagine horrible consequences to one day siding with their girlfriend or boyfriend, but really, the worse that would happen is an argument where people actually speak their mind. And that's not on the same level as abandoning your children or letting everyone down at a job that depends on you.
So when people have obligations, it's definitely important to take care of them. On the other hand, it's good to keep in mind that your girlfriend, for instance, is not responsible for the fact that you have children, nor does she get the same benefits from them as you do, unless she's already a primary. Maybe she would want her own children with you and it's impossible. So this can still be a privilege you had, to have children with that first partner because it's socially acceptable, when the second partner doesn't have the same option. Sometimes even if the married couple has no children and they want some, and there is a girlfriend who also wants some, it seems to go without saying that the wife can get pregnant but the girlfriend isn't allowed to, ever, even after years together.
It's good to look at it and keep in mind that it could be about privilege.
People might say "if I have a child with my girlfriend and people realise we're poly, the kids might be taken away from us". Yes, it's true. And that's still privilege. A mono couple has the privilege of not getting their kids taken away. As I said, a privilege sometimes really is something that everyone should get to enjoy.
If you refuse to be out because you don't want your kids taken away from you, it's absolutely a reasonable decision. BUT it still means that your non-official partner has to hide so that you can keep your privilege. And that doesn't make you a bad person, but it sucks, and it's good to at least know and understand that.
I think people usually understand that the whole issue with "privilege" isn't about the person who have it, but the whole of society treating some people as second-class citizens. I think one big deal is to acknowledge that your partner is being treated as a second-class citizen, because you hide them, because you're afraid of also being treated as a second class citizen if you didn't hide them.