What we need is more of an "agent" like actors have: Maybe I don't have a full picture of what a Hollywood agent does, but I imagine they're constantly working in the background, looking for gigs for their busy actor, doing all the toil and paperwork and research on their behalf. Their end product is: "Studio X wants you to work on film A this year, and then Studio Y wants you to work on film B next year."
I could see a software engineer agent who gets paid by the engineer to do all of the application-filling-out, all the LinkedIn clicking, all of the company research, all of the pavement-pounding networking and paperwork toil, and all the interviewing, and then out comes: "Companies X, Y, and Z have these offers for you, which one do you want?" I'd probably pay a fortune, or maybe even a percentage of my comp, for a service like that.