It looks like most people hit it so I don't want to beat the dead horse. I don't even use VBD anymore quantitatively, but let's assume I do for the sake of discussion. ADP is immensely important to know who should be there for you in certain rounds. It effectively allows you to map out a draft strategy ahead of the draft of the pools of players available to you in each round. Going into a draft I will likely be able to call what my team will look like with over 70% accuracy. ADP allows you to mock different strategies ahead of time to allow you to build the best team on draft day, knowing who you can get when.
This has three facets, some of which has already been discussed.
The first is if you project a player much better than the masses (you have Player X going being your top pick in the 2nd round, when ADP has him in the 4th). This allows you to pick another player in the 2nd, you can get your guy in the third, and in theory as long as you are correct in your projection, you just drafted 2 second round picks. The value of that is huge.
The second is knowing that a guy you really like on the board will not be there the next time you draft. Maybe you are taking him "early" 7 picks before ADP, but if he won't be there the next time you pick, you may as well grab him. This has value as well.
The third is somewhat based on DVBD where I will have a round by round analysis of how many people at each position are taken in a round. I don't care about names here, just the number of RBs, WRs, etc. This has a great value in being able to see runs on positions and how your current draft is deviating from that. If a WR run typically occurs in the 3rd round, but hasn't yet, you know it is coming. You can estimate how many players at each position will be taken in between your picks and get a handle on what the dropoffs at each position will be. I no longer do this quantitatively when I draft, but I do look at it and make decisions based off it.
Ultimately people are right in that if you draft good players you will be the best off. Unfortunately we all have an error rate in our projections and drafting is an in-exact science, and really I would call it more art than science. After trying to quantify everything in a draft, I have realized that the numbers need to be crunched before a draft and when the draft starts it all comes down to analyzing projections and how they relate to your scoring system and going with the flow.
This is why I like to be near a turn, but not on a turn. I can look at owners' rosters and from who they have taken previously I can manipulate that information into taking a guy I might take in the 5th and wait until the 6th based on who they have. This allows you to slowly chip away at other teams increasing your team's value.
VBD is good to know in theory and to understand what it means, but ADP is more important than VBD as it gives me information as to what other people will do, and I am able to manipulate that to my advantage.
So many people refer to people they draft as "starters" and "backups' and a lot of people use VBD based on last "starter". In my mind, there are no "starters" and "backups". Everyone I draft has a good likelihood to start at some point. If you play in a start 3 WR league, you will likely be playing your WR5 a good 25% of the season, if not more, and will play your WR6 as well. To ignore this as an overall draft strategy and draft defenses early or QBs early based on some arbitrary baseline is extremely flawed. Now you may draft defenses early or QBs early because your overall draft plan based on ADP around your picks allows you to build in your mind what the best team is. However most don't do this, just look only at the round they are in based on VBD, draft, and then worry about the rest later.
Using ADP in connection with VBD is effectively DVBD (dynamic) which is inherently better than SVBD (static). In fact, if you are a VBD purist, you should be pushing to use ADP as it takes your analysis to the next level as many people here have said.
If nothing else, if you can zig while the masses zag, there is value in addition to enhancing your VBD analysis.