I'm an electronic engineer turned software engineer and have been doing this for decades. I am in the Midwest USA, a large city but not a high tech one.
I used to be contacted by headhunters at least once a week. Nowadays, I hear from Indeed and LinkedIn that often. I have been to their offices for interviews and assured they would find me a job quick.
While I have risen through the ranks over the years to project manager and a prolific company and, eventually, ran my own profitable company, I have never, ever been sent on an interview anywhere by any of the operations I mentioned above.