I'm really just reposting this part of your comment because of how strongly I agree with this.Allow me to be perfectly clear: There is absolutely no honor or utility in adapting to a custom so deeply and thoroughly broken as the modern hiring process. You will get a job by going "nice company you have here, I think I'd like a job" until someone says "...yeah okay that works for me." I'll go one further - based on what I've seen and the trends I've observed, it will work this way for the duration of your career. Get used to it, get comfortable with it, and accept that employment is a partnership. You're giving up a big chunk of your life so you should get a big chunk of their money. They aren't doing you a favor, you aren't "lucky to have the job", you have skills, they have money, it works out in their favor, don't ever forget that.
Adding to the train of agreement on this, there’s also no shame in following up with those that you get declined a position from to ask something in the form of: “Can you refer me to a department within the company or otherwise that is in need of someone with my skillset?” Preferably this is over the phone with the hiring manager, but it works just as well with an e-mail (assuming you have the e-mail of someone other than HR).
Piling in to agree with that. While not the exact same scenario, we just finished another round of interviews, and one candidate was awesome but didn't like the sound of any of the roles we initially wanted to interview her for. Many people might accept a job as it's a job, but she was brave and said "This has been great, but they're all very clinical focused roles and I don't know if I want to leap into that." and I said "Cool, appreciate the honesty." and she asked if there was anything more focused in supporting academia. I said I'd check and get back to her. Called a colleague across campus, sure enough they're jonesing for someone bright and capable. Passed on her number and they had a less formal interview the next day. Pretty sure she's hired now. Anyway point being, no harm in asking.