Asking for the job is conventional wisdom for interviews in the white collar world, especially if the position is sales or influencer, they will expect you to not be shy about asking for the sale (sales 101).
Not really required or expected in aviation, unlike white collar where you may have invested minimal time and effort into the interview process, at an airline interview they know you prepped, did your logbook, filled out reams of paper, traveled halfway across the country, etc. In aviation they are not looking for aggressive BS artists, they want to evaluate you on what THEY think is important (which includes interpersonal skills).
As Qotsaautopilot pointed out, you're not really competing with other applicants... most airlines today are prepared to hire all interviewees, unless they trip on their own crank.
In white collar, there's usually only one job and likely multiple applicants, so you need to be more aggressive... if there's no clear standout it might well go to the guy who sold himself harder.
OK, and probably good, to make a strong closing statement if they give you a clear opportunity, but don't force it if it's awkward.
Also... if you're undecided on whether you actually want the job... don't let that shine through or weaken your enthusiasm. Once you get the job offer, THEM you can make up your mind.