Betteridge’s law applies here: the answer is “no”. It’s a subtle “no”, though.
As a scientist, you will always need to be able to communicate your work. Most of the time you can get away with papers and talks aimed at your peers. But the longer you mean to stick around, the more often you will have to justify yourself to others: to departments, to universities, and to grant agencies. A scientist cannot survive on scientific ability alone: to get jobs, to get funding, to survive, you need to be able to promote yourself, at least a little.
Self-promotion isn’t outreach, though. Talking to the public, or to journalists, is a different skill from talking to other academics or writing grants. And it’s entirely possible to go through an entire scientific career without exercising that skill.
That’s a reassuring message for some. I’ve met people for whom science is a refuge from the mess of human interaction, people horrified by the thought of fame or even being mentioned in a newspaper. When I meet these people, they sometimes seem to worry that I’m silently judging them, thinking that they’re ignoring their responsibilities by avoiding outreach. They think this in part because the field seems to be going in that direction. Grants that used to focus just on science have added outreach as a requirement, demanding that each application come with a plan for some outreach project.
I can’t guarantee that more grants won’t add outreach requirements. But I can say at least that I’m on your side here: I don’t think you should have to do outreach if you don’t want to. I don’t think you have to, just yet. And I think if grant agencies are sensible, they’ll find a way to encourage outreach without making it mandatory.
I think that overall, collectively, we have a responsibility to do outreach. Beyond the old arguments about justifying ourselves to taxpayers, we also just ought to be open about what we do. In a world where people are actively curious about us, we ought to encourage and nurture that curiosity. I don’t think this is unique to science, I think it’s something every industry, every hobby, and every community should foster. But in each case, I think that communication should be done by people who want to do it, not forced on every member.
I also think that, potentially, anyone can do outreach. Outreach can take different forms for different people, anything from speaking to high school students to talking to journalists to writing answers for Stack Exchange. I don’t think anyone should feel afraid of outreach because they think they won’t be good enough. Chances are, you know something other people don’t: I guarantee if you want to, you will have something worth saying.