Yes, a DoF has to be judged on their recruitment, amongst other things.
Allen has an average recruitment record.
However, recruitment was not Allen's strength.
Allen's signings: Docherty, Middleton, Murphy, Cummings, Martin; Arfield, McGregor, Katic, Goldson, Flanagan, Barasic, Lafferty, Grezda, McAuley, Kamara, Ejaria, Sadiq, Coulibaly, Kent, Worral, Defoe, Davis; Hastie, Jones, Stewart, Edmundson, Aribo, Helander, Barker.
(I reckon there are a few more shockers that I've missed.)
What's that, 10-11 first-team players? And, a few good youth prospects. That's a whole new spine to the team. It's actually not bad at all -- although, the failures are really bad!
Like I said, recruitment is not actually his strength. I believe Wilson is actually a better recruiter.
There was a story the other day about the Lille DoF (Luis Campos, one of the best https://www.skysports.com/football/news/11095/11830121/luis-campos-the-transfer-chief-with-the-midas-touch), where he suggested Man Utd were an example of a team in need of a DoF: no overarching strategy, or recruitment policy, causing them to make bad decision after bad decision. Mourinho wanted a DoF, because the culture wasn't right: it didn't have any cohesion.
If you appoint a good manager, that can do everything, then you're in great hands. But, that's extremely rare. How many Alex Fergusons have there been? And, then why would you take the risk of ripping everything up when they leave after a couple of years?
When Gerrard leaves, the structure in still in place, so a manager can slot right in with little disruption.
In the modern game, a DoF is absolutely essential.