Is there a tactful way to let a job know that their interview style turned you off and made you not want the job?

I think the answer is "no." There really is no way to speak to them about this, except perhaps in the event that they offer you a job and you decline. And even then... yes, all you can say is "my experience in learning about the workplace makes me think it's not the right fit for me." (Been going through this with a friend recently, so we've talked a lot about this.) You don't know in what situation you'll run into any of these people again, for one thing. So being misunderstood and being "that weird jerk who was mean to us" or whatever doesn't serve your purposes in the future. Should anyone ask you for feedback (at the agency or elsewhere), this is valid to give. But we think the general principle here is to keep your counsel to yourself, particularly if it's unasked for. (I have a hard time with this myself! A very hard time!)

If I found a genie in a bottle and had three wishes, I feel sure that one of them would be to go back and not take a job where I ignored red flags during the interview process. Actually, this happened more than once to me, so I feel pretty dumb for not learning this lesson faster. So my hypothetical genie would actually have to look at me and say, "which one?" Since these jobs turned out to be all they promised on paper, but were absolutely horrendous in other ways I never saw coming, I would be hard pressed to choose. Anyway, the moral of the story is if you feel put off and uneasy after three hours in the interview process, run and don't look back. I would not try to change them by letting them know that you thought they handled this or that badly and turned you off. At best, they'll probably blow it off and, at worst, it could burn a bridge you may want to cross later. If I were you, I would write a nice thank you note letting them know that you appreciated their time (and maybe add a little something about how much you think of their organization and the work they do, since that is true) and say that you have accepted another position.

Is this typical in some countries? I'm an Australian, and that seems pretty typical to me of a public sector or larger community sector job interviewing process. Job interviews are done by selection committees who don't all necessarily know the specifics of the job you'll be doing: the committee is given specific criteria and makes a selection amongst the best qualified or suited people only according to those criteria. That's all. It might not be appropriate, in the organisation, for the people interviewing you to sell you on the job, and it definitely wouldn't be appropriate for them to try to win you in particular over, above other candidates.

I have traveled 6 hours for an interview, being told that I am an idiot, that they don't need me and that they have much more qualified candidates and traveled 6 hours back. Yes, sure, it can be rough. It wasn't in the US and I actually think it may be common to just walk out on a condescending interview. I heard of someone in NYC who had 10 (in words TEN) interviews for a job and then got rejected. TL;DR It is a buyers market!

They will either not catch on or think it's sour grapes if you say this before the interviewing is over. You do have one chance to make an impression, and that's when they offer you the job and you turn it down and explain your concerns about the culture. That said, you might as well say something in an e-mail if you don't get selected. It's tactful enough to not burn any bridges, and there's a non-zero chance it will have some effect.

I think that you are saying that your primary concern is that you didn't get to ask questions. If that's the only big concern (and it might not be), why not try to arrange 30 minutes to ask more questions in person or on the phone. As far as turning down the job... if you know you won't take it, I would just let it go until they ask you to do more interviewing. At which point you can simply state that "Component X" doesn't seem like a good fit for you, which will give them the opening to ask you to elaborate if they want. I have told interviewers that a salary seemed below my negotiating range, for example, and some asked for specifics, and some didn't.

Some smaller organisations are normally well run and organised - but prone to having their interview process spoilt by occasional events that create chaos. If the people you talked to happen to fit into this category then they might be receptive to your message. Other organisations are just badly run and permanently chaotic. If this is the case then I believe you are wasting your time pointing out mistakes to them - just move on. It is worth trying to make a guess as to which type you were dealing with.

I'm an Aussie working in public sector, and no, this isn't par for the course. So it may be culture, but definitely not Australian public sector culture. I had some red flags for the current job, and wish I hadn't taken it, but lack of description/no questions was not a feature of the interview process. They weren't overly truthful about the job, but they were descriptive amd the question section is built into every job interview I've been part of.

I also had an interview with a foreign-staffed non-profit whose mission I care about and in which the interview process was off-putting in exactly the same way, and I also wondered if it's a question of culture. I never found out: I took myself out of the running because the vibe was just too unpleasant and it wouldn't have been worth it to me to continue.