Working with adequate privacy and quiet does not mean the same thing as holing up away from everyone. I still enjoyed talking shop over lunch, jumping up from my desk to go and assist someone with a bug, attending research and tech presentations, and all the other good stuff of being in the office.
I also feel I am not well-suited to consulting because I significantly prefer to work with a more or less stable technology stack, in which we invest time to properly refactor, write tests, and design things so that the system we maintain and grow over time can easily adjust and expand for new business needs and new functionality.
With a lot of consulting, especially in my area (machine learning and scientific computing) you are always at the mercy of whatever technology stack you walk into, and whatever state of disrepair that code base is in.
In a lot of consulting, there can also be unforeseen traps. Sometimes you can get into a situation where a client can require you to come to their office, or work in some other sort of field site situation that is insanely horrible, and you can't get out of it without basically quitting and thereby burning a bridge and negatively affecting your consulting reputation.
Just because I happen to have a strong preference for mental health affirmation through adequate privacy and quiet doesn't mean I am looking to bottomlessly compromise on all the other working standards I have too, such as quality of the work, adequate pay and benefits, and so forth.
Unfortunately, no one has even offered me these other compromises. No one has said they would consider a private office if I accepted less pay, fewer vacation days, etc. They just simply say it is in principle impossible.
But I don't know of any other way to ensure that I can have the adequate privacy and quiet that truly is physically necessary for me. I've just come to accept the fact that this means extremely lengthy job searches for me, and a need to do the really hard thing and reject some otherwise pretty good job offers if they can't provide an office.
Edit: sorry, it sounds like that's what you're doing already. Just re-read your post more carefully. Anyway, I wish you good luck in your search and I hope you're able to find a suitable job situation. Maybe it would help to classify this as a disability somehow? I think they have to provide "reasonable accommodation" under the ADA act but that could mean a pair of noise cancelling headphones.
There's a ton of quantitative evidence supporting this. Yet employers persist in only ever buying open-plan space. Established companies that already had private offices sometimes even spend money to tear down the privacy features and remodel the office to function as a type of fashion signalling that they are "cool" like what they perceive start-ups to be. So they actually pay money to destroy productivity, so they pay money to move their business into a state in which the business makes less money.
Then you also see firms spending money on needlessly opulent lifestyle masturbation, like moving their office to some expensive downtown location with a roof deck. Or building a rock climbing wall in the office.
So you know it's not an issue of lacking the money for buying real estate that would support private working conditions. It's just a lot of issues about status and opulence.
So while you're correct that given their current office layout they might be unable to accommodate giving someone privacy, it's disheartening that they were ever in that situation to begin with since it would have been demonstrably more cost-effective for them to have built privacy features into the workplace from the beginning.
It has really caused me to see office space as a major red flag about a company. It says a lot about what the management of that company cares about.