It makes me think that personalized rejections - for short stories submitted to journals, at least - are very, very rare.
I would say about half of those rejections included some "please submit to us again" sort of language, and the other half did not; into that I read exactly nothing. It's possible that editors put thought into whether or not to include such language.
The general impression I get from reading around the topic is that personalised rejections are rare.
But from my own limited records (about 35 rejections), I get the sense that some particular magazines give personalised rejections much more often than others.
With some magazines that I've submitted to a few times, they seem to give responses that are halfway between a personalised rejection and a form rejection.
For example:
"The beginning was good, but [form rejection]"
Or
"The prose was good, but [form rejection]"
So they're nothing truly specific to your story (such as "I liked how you brought out Sarah's hate for her mother in the beginning..."). But it's still more specific than "This isn't right for us."
That could mean they have a bunch of comments at the ready for common issues, and it saves them time to just paste them in.
Or it could be that these are individually written personalised rejections – but they're brief and vague because the poor editor has a thousand stories to read each week
Recently I've gotten a couple of higher tier rejections from a magazine I'd love to be published in. Was just wondering are higher tier rejection actually a thing or are they merely a courtesy? I wonder how many higher tier forms a semi pro magazine sends out per month? I'm guessing quite a few?
I've had a string of identical rejections from one magazine – something like "Not for us, but good luck with it wherever you send it."
And then on one story, the message from that magazine changed to something like "Good job with this one, but it's not for us. Looking forward to your next attempt."
I'd call that a higher-tier form rejection.
Adding higher-tier rejections just "as a courtesy" wouldn't really help anyone – neither the magazine or the writers.
They're probably exactly what they say in the message: a small sign that your story wasn't rubbish, and a hint that you should keep trying with them.
I can't imagine that they have any set target or limit on the number of different types of rejections they send out. I don't see how that would benefit them.
I'm sure there's a natural limit to the number of personalised rejections (just due to being too busy).
What do you mean by "Are they a thing?". If you've got some – and you said you did – then they're a thing