I think that most placement offices at most colleges tend to have jobs in their cities or states. Do they have listing for jobs in other states, for the government, in NYC? Sure, but the majority of listings at Ohio State are going to be in Ohio because that’s where most grads want to live.
My daughter went to school in florida and her first job was in Florida. She applied to a big national company but the office that got her resume was in Orlando. She said she was interest in traffic and they said “Oh, that’s out of the West Palm office” and sent her resume to that office. Now she works for them in Denver (transferred). Could she have, on her own, applied to one of their offices in AZ or CA or ID? Yes, but she couldn’t sit back and expect the placement office to locate jobs in those areas for her.
I think your child is going to have to work a little harder to find a job in the US after going to school in Europe. Will the school post the jobs if the employer gets the info to the placement office? Sure. Will the placement office actively search for listings in Oklahoma or California or Texas? I doubt it, just like the placement office at U of Delaware isn’t going to focus on getting listings in Idaho or Utah.
So many initial job interviews are now done by zoom that it doesn’t matter where people are. My SIL just applied for a job and had the initial interview while he was on Nat’l Guard duty in the desert in CA, he lives in TN, and the job is in TX (don’t know where the interviewer was located). It’s a different world now. He happens to be going to grad school online at a Texas school, but that is just a coincidence that this job is in TX as SIL never ‘attends’ class in TX (and my daughter doesn’t particularly want to live in TX).