Some people don't understand how Woodward has failed. They think that he shares blame for the short term on the pitch performances and thus any manager under him is doomed to not get the best out of the players.
Woodward is to blame for this mess, but not the performances. Here are his failings that led to this mess.
1. He's very slow to cut off a manager that clearly isn't working.
2. He has given the manager too much power
3. He has no consistent vision for what he wants United to be except successful.
4. Because a combination of #2 and #3, his managerial appointments have all been stark contrasts from one another apart from the fact that they're conservative. This has led to players the next manager has no use for.
If he doesn't come up with a direction the entire club can rally around (this includes supporters), then he will repeat these failures again. This extends to managerial appointments, inconsistent player turnover, etc... Because of this, it is more likely the next manager does fail.
But there a difference between what I just said and what those people who say there is no quick fix. The manager is directly responsible for the on pitch performance because he's the one who gets to invest in certain players, he's the one who is responsible for motivating players, he is the one for how the team sets up, and he's the one who is responsible for how the team reacts to what's going on the pitch. The manager is directly responsible for the performances unless Woodward doesn't back the manager from the get go or he creates so much drama that he's simply a distraction for everyone at the club and the club becomes an unprofessional work environment. In conclusion, Woodward being a failure means it's more likely that the next manager isn't the right hire, not that the next manager is automatically doomed to fail.
For all we know, Woodward learns from his mistake or he just flukes the correct managerial appointment and this next manager is what everyone wants out of a manager. Next 2 managerial appointments will be very telling whether or not he has learned from the last several years.