I don't think it's necessarily peers, it might be any humans that we interact with as a part of our work - our bosses, our clients, etc.
If anything, the reason why burnout seems to be more frequent is because too many people care too much about their work, which creates pressure on others to join in on appearing like they care and emotionally invest in their work, which goes back to my theory that people ultimately burnout because they’ve been pressured to put their whole selves into their work when for many their work is actually devoid of much meaning.
> which creates pressure on others to join in on appearing like they care and emotionally invest in their work
I don't see this pressure coming from people who care. I mean, they want others to care, but they certainly don't want them to be pretending it.
So if anything, this pressure comes from within you, and then it also can be considered an issue of emotional control, but it is a different issue than caring too much about your work.
In other words, it seems like there are problems on both ends of the spectrum. I care more than average person in the group => potentially an emotional problem for me (that's my explanation of burnout). I care less than average person in the group => potentially an emotional problem for me (that's your explanation of burnout).