I totally disagree. I also think D3 already had mismanagement problems back then: the game was delayed 6 months putting it right between Far Cry and HL 2, they had schedulling issues with Trent Reznor, last minute changes to the shotgun, the final game had very little gameplay or assets from what was shown at E3 2002 (the leaked alpha), etc. Their management problems only increased as they decided to grow their teams. Then they worked on that Darkness game for 1.5 years only to cancel it and go for Rage all the while having to supervise Raven with Quake 4 in 2002-2005 and then Wolfenstein in 2006-2009, help out Splash Damage with ETQW in 2005-2007, coordinate the various companies doing the ETQW/Wolfenstein console ports which also suffered from management problems themselves, mess around with Quake Live, mobile games, rockets and God knows what else.
That Kotaku article finds me... impassive. I don't know if the specific anecdotes are true, exagerated or whatever but the overall storyline of DOOM's development matches exactly the same problems we've been witnessing from the outside for the last 10 years. In fact, for the last 13 years as DOOM 3 was announced back in March 2000 as a neccessity as Paul Steed was fired because he wanted to do a new DOOM while two of the owners Adrian Carmack and Kevin Cloud did not. Romero's firing after Quake's release also spawned from fundamental business practice differences (not just Romero being a lazy bastard who wanted to DM all day instead of designing levels like he was supposed to). You could probably even go back and find even more management problems.
If you have a small team, management issues may hinder but usually will not bring down a project. That's no longer true with bigger teams, longer projects or multiple companies and especially not when you have amateur managers (artists, level designers, programmers who were promoted to managers - experience does not always replace knowledge).
Aside from management issues, there's also the remarkable trend that culminated in this 2011 DOOM reboot. After DOOM 3, id decided to focus more on the console versions where Quake 4 had a piss poor, buggy and slow xbox 360 simultaneous release and Rage was basically a console game ported to the PC. This trend correlates almost directly to the sales numbers of each game.
The more Carmack got on a pulpit extoling the virtues of multiplatform development and how companies HAD to focus on consoles if they wanted to turn a profit, every new game either developed or supervised by id that was more and more console focused sold less and less than the game before it. I do believe Rage sold more than Wolfenstein (2009) but pretty much any other game would, let's be honest.
Maybe id could take a few cues from DICE which had a resounding critical and commercial success with BF3 despite the fact DICE constantly said the PC was the lead dev platform, how they honestly and openly said the PC version would be better than the console versions (graphics and gameplay features -wise) and still managed to sell quite alot of copies on all platforms, going directly up ahead with the behemoth of the industry releasing nearly at the same time as the CoD of the year.
Compare that to DOOM 3: BFG edition where the PC version doesn't even have uncompressed textures like the original PC DOOM 3 had 9 years ago!
id has to fix its management issues and you do that starting at the top, not shuffling people around teams. Who did the shuffling? The same amateur managers who shipwrecked multiple projects already?