There are two strongly connected but still a bit controversial things in the industry that makes this kind of question being asked all the time since 2010.
First one is a nature of DevOps methodology itself. It was born all around idea of better collaboration between different parties of software delivery process. This involves a lot of non-technical aspects, like shared responsibility, better communication, knowledge sharing. Another improvement that was aimed - was product delivery itself, starting from designing software and up to deployment and operating live systems. So it brought us technical improvements as well. There was nothing new, actually, as all those things you see in majority of “DevOps job openings” like CI/CD, configuration management, log management, monitoring, whatever – were existing for decades, before even term DevOps was used for the first time.
So DevOps as methodology just put all this bits to one plate.
And here comes the second thing: hype.
Popularity of the methodology arisen - as it was intended to solve problems that majority of industry players had more or less. So some people started to see non-existent “silver bullet” here. Some magical potion, which simply could solve issues they have.
So we got high demand here. And as a result – supply started to grow as well. And obviously businesses were looking for someone who could implement “DevOps” for them. How do you usually initially identify someone who could work with some tool/methodology/whatever? I bet - the answer is - by looking for appropriate badge in their CV:)
People realized, that being badged as DevOps engineer, not simply being a sysadmin or developer – makes them more unique and valuable on the market by that time. That is how market works overall - you make offering and advertise what demanding person is looking for, so he prefers you as a supplier, not the other guy.
And somewhere here we got that focus shifted from whole methodology to technical side of it. I have no exact answer, why this happened, probably because majority of market players missed the key point of DevOps ideas, and understood only those which could be measured easily.
Do we have Jenkins running now? Tick!
Do we use Chef/Puppet? Tick!
It is way harder to make same kind of measurement for collaboration between team members, communication improvements, whatever. And higher management usually looking for kind of measurable results, rather then ephemeral ones.
So you are absolutely right – DevOps should be done by everyone in a team, just because it is about team itself, not some person who makes changes, and everyone and everything else remain old-fashioned.