I’ve heard it said that the Doctor choosing her companions this season seems more random (in a good way) than the way they have selected them in the past. Which is generally true, but I also think these people were chosen by accident because of their kindness.
The first time she meets them they’ve encountered this terrifying alien tech ball on a train and instead of running they all decide to help (Graham is kind of voluntold to help, but he still stays). And they didn’t have to! The target guy left and no one complained, but they stayed to help.
And not only that, they all volunteered to help her as she adjusted to her new self. Giving her a place to rest, taking her shopping for new clothes, helping her build her device to get to her TARDIS.
Then at the end of The Ghost Monument, she strands them all on an alien planet and what do they do? Do they get mad at her? Nope. They instantly try to encourage her, and tell it will all be OK. (and then it is). (And they spent the whole episode stuck there and never once got mad at her for it.)
Then in Arachnids in the UK she only stays because Yaz recognizes she’s lonely and invites her to Tea.
They are constantly treating her with an enormous amount of kindness and understanding, even when she’s colossally screwed up. They are all about as soft with her as she is with them (bantering aside).
AND they are also all super kind to the other people they encounter as the series progresses.
We have Yaz empathizing and bonding with someone in almost every episode (it’s a really long list, that could be its own post). The most obvious two are Willa (who actually calls to Yaz for help when she’s scared and not the Doctor) and the guy at the factory (who she kept the necklace of to bring back to his daughter). But there are several more.
We have Ryan comforting Graham on more than one occasion about their shared grief over Grace (and Graham encouraging him in 11x02 with a memory of Grace). Ryan who is the first one to say I love you to both his granddad and his dad. Who volunteers to help a stranger deliver a baby.
We have Graham who also volunteers to help the stranger deliver a baby. Who is sure to tell Prem that he’s a good man before his wedding. Who tells Ryan he’s going to protect him in the Ghost Monument. Who tries to help Yaz make sense of her meeting with Umbreen.
ANDDD they also encourage her to be kinder too. Like in Kerblam when she sees Ryan standing up for Kira and follows his lead. Or at the end when it’s Yaz’s idea to bring the necklace back to the factory guy’s daughter.
(and as an aside, this may also be a big reason they don’t have a lot of major conflicts between them in the series. Because just like it’d now take a more emotionally mature Doctor a lot more to snap, I also think it’d take this emotionally mature group a lot more to become confrontational with each other. Not saying it can’t happen in season 12 but it’d take something big)
So though I agree that, yes, they were chosen a lot more randomly than people in the past, I also think the reason they stayed on with her for so long is because of their kindness and willingness to help a stranger. It wasn’t that she decided “oh these people are neat I’m gonna keep them” it was more that they decided “Oh she needs help, let's help her” and then eventually it was them who decided “We like this one, let’s ask her if we can stay with her”. And she said yes because she liked them too. Because they are just good people who are nice to be around and who inspire her to be better too.
It’s really, making friends in kindergarten simple, but also very beautiful. And one of the reasons I love this season (series?) so much.