Errr... not me, no. My DC will never have step parents.
I was speaking rhetorically, not towards you specifically.
Of course it benefits the new partner. Presumably they care about their partner and want them and their children to be happy and comfortable with the new setup? This tiny amount of effort and time will help immensely with that in most cases.
.... Again, what has it got to do with those people? It's not her partner or the kids who it would make feel more comfortable, it's the ex, it's for her benefit. Why would her partner be uncomfortable they hadn't met? It would be pretty tangential to say it benefits the new partner because it benefits her partner and the kids, anyway, but it doesn't even benefit them! There's no "of course" about it...
Children are a lot happier and settled when living between two homes if parenting and boundaries are consistent between them and all adults involved co-operate together so if the OP sees this relationship progressing to living with her partner and being there when the children are at their home with their father then surely it's better for everyone to have happy, well adjusted children who don't feel uncomfortable or torn between parents who aren't communicating well with all of the behaviour challenges and stress that would bring, and that the children feel comfortable talking about their mum to her, and about her to their mum.
All that may be so, but far more relevant if they are going to have ongoing communication. Not the 20 minute meeting you described. The ONLY purpose of that is to satisfy the mum, and the only reason a 20 minute meeting would help the children not feel torn between their parents is if without that meeting, the mum planned on making it clear to her DC that she has a problem with their SM. That's entirely on her to control, she does not have to do that. She can make them feel just as comfortable if they'd never met as she could if they had met for 20 minutes.
It might not work in every situation but why would someone NOT want to make this tiny amount of effort to get things off to a good start and reduce the risk of things become difficult for the children and them and their partner?
It's not a tiny bit of effort meeting up with someone that is behaving in a rude and entitled way towards you. That is my point. It might be a tiny bit of effort if they were polite and gracious. And again, the only way things would become difficult for them without this meeting, is if their mum chose to act unreasonably out of petulance due to not being granted a 20 minute meeting. That is on her.