If you already have a QB, you pick BPA regardless of positions or needs. When you start reaching for a need over talent, you end up with less talent. We NEED defense, but if the Cowboys have an offensive player rated the highest when we pick, that's who they'll go with.
We didn't *need* Ezekiel Elliott. McFadden had over 1,000 yards the year before. He was the BPA (according to our board), so he was the pick. Look how well that turned out.
That all sounds great, but it's not that simple. First off, the BPA is a discussion, even within the war room. Secondly, you mentioned QB, which is absolutely true, but there are other positions that have greater meaning, depending on the team. Thirdly, your team may have a glaring weakness, or if you'd rather, a fatal flaw, or flaws. Finally, you have to consider the depth of the draft.
When you stack your board of BPA's, a lot of these factors come into play, and are built into your board. If you rank the first 300 players, and are checking them off your board as the draft goes, you don't pick a DT, if he's only ranked 5 players higher than a position of need, especially if you are stacked with DT's. Nobody does that. That being said, the top ten players are usually different, and the factoring becomes exponential as you go. You probably wouldn't drop 3 - 5 places on your board in that area, except for the aforementioned QB position. Midway through the round, you might drop 5 -10 places if you find the talent, need, fit and position of importance on your team.
In the 2nd round, you might go 10 - 15 for the same thing, because all the things I mentioned, plus in the later rounds, depth can be a factor on draft position, if you haven't already addressed it. If you only have 2 more projected starters at a position, of importance, and need, you may have to push the envelope a little, because you know you won't be able to address that position in later rounds. Remember though, your team has these players projected as the right fit, and potential starters on your team. If you try to get too cute, you miss out on the Bobby Wagners.
Even after all that, it's a flawed system, because your scouts make mistakes; you can't measure heart, or growth in some cases; it's hard to evaluate the capacity to learn; character issues can go unseen, and you can't always plan on injuries.
You hear BPA a lot, I just think it's way more complicated than that, and it's rare to find a consensus, especially once you start burning through the draft.