I have one, and keep it pretty well updated.
As a general rule, when there are many EMS providers who don't know how to write a resume for themselves, I think having a LinkedIn profile can be beneficial. While yes, most EMS employees get hired by applying on the company website and going through the process, having the profile allows you to add much more content than can fit on one or two sheets of paper, provided you include a link to it on your digital resume.
I have several former coworkers on my linked in profile, as well as many non ems coworkers. I also know people who have been at the same job for 10 years, and will never go anywhere else (for various reasons), so having a profile is useless for them.