Yes, you do.
As the social media world keeps reminding us, every time we post and tweet, we are establishing our personal brand. And with so many online channels focusing on photos plus text—if not photos exclusively—you simply have to be able to come up a clean, clear headshot to put a face—that being your good-looking face--on your brand.
Here at Special Events, the web platform we switched to earlier this year not only requires at least one image for many type of articles we post, but much bigger photos than we used to pester you to send. (We used to ask for headshots that were 30KB, but now we need at least 1 MB.)
As Madame Editor, I suggest you avoid a selfie. Because they always look like selfies. We talk about business issues, and so we don't want anything that looks too much as though it was made by loving hands at home. Such photos suggest either that you don't really care about your profession or that you don't have enough in your own marketing budget to get a decent professional headshot.
So spend the money and get a good headshot. Then get ready to go viral.
(This great headshot is from White Balance Photography. Those who know me know this photo makes me look better than I actually do.)