I think you have to bridge the gap between the two. The plus of needs-based drafting is that you're going to get a higher percentage of your draft picks wind up being contributors, i.e. you're going to hit a lot of singles and doubles. But the BPA approach means that you can get top-level players, and thus you have the ability to hit triples and homeruns.
I think the happy medium is the way to go. And that's hard to do, but I think it largely means that you skew more towards BPA in Rounds 1 and 2, and then probably shift to need more in Round 3 or later. Although I think too often you can shift too much for need in Round 3, when there is still earlier round talent available.
I think the issue with the Falcons has less to do with need vs. BPA, but the fact that they don't do a good job self-evaluating their roster. I think they don't do a great job targeting guys that are going to excel in their schemes. That's the key to why some draft picks work out, particularly in the middle/late rounds, because you find guys that are near perfect fits in yoru scheme.
And that's something I think the Falcons have rarely done. My oft-used example is Sam Baker, but Jacquizz Rodgers is another great example as well. This team tends to be more about adding complementary and role players than it is about playmakers. And I think the lack of playmakers is what is holding this team back from reaching their goals. And it's sad, when they paid a huge price for their one true blue dynamic field-tilting playmaker, and they only want to use him as a complementary player. For any other team, he woudl be their Larry Fitzgerald, Calvin Johnson, or Andre Johnson. But for this team, he's just Michael Jenkins on steroids.
I think the bridge is BPA across multiple needs. So you don't draft a QB if you have one, you don't draft an LT in the 1st round if you have a 2nd year guy who is great.
But, this year, for instance, were the OL shored up a touch, you'd have DE, S, DT, OLB, WR, TE, RB, OT. That's a lot of guys, you'd sort by round, and you'd know DE replacement is more critical than DT replacement for instance, but basically...wouldn't a DT who can contribute year 1, and you get an early 2nd round talent in round 3 be better than taking a DE (or LT) who you have 4th round graded (this is hypothetical.) An athlete, a starter or strong rotational caliber player, at WR, RB or TE would have made a big difference to the offense this year. A DE or S or OLB who you think can be a legit starter could get legit reps year 1, and then be an answer.
I think with the rotation, you have a lot of options for guys who can contribute year 1, but have a likely chance of starting the next year. But if you just have 2 or 3 positions, and you MUST take them, you're nearly certain to reach on the last one, if not two.
I don't count the 5th-7th rounds. I frankly think those are generally for boom/bust type picks who you can groom for a year and see what you have, or for role players. I don't quibble with those too much, unless it's a limited athlete at a full position.
But I will agree the self assessment hasn't helped anything. The things you mention are the things that make me feel like, despite collaborating, TD and MS aren't exactly on the same page.