Sorry, we're not ignoring this thread; we've just been very busy!
I just launched OmniFocus on my iPhone (from the home screen), and according to my stopwatch it took 4.9 seconds before it was ready to accept input. (I currently have 1,124 tasks in my database.) I launched the built-in Notes app (which is much simpler than OmniFocus), and it took about 4 seconds.
Now, I know that OmniFocus doesn't always launch in less than 5 seconds—and we're busy working to make OmniFocus load faster, sync faster, and to let you immediately switch over to adding a new inbox item without waiting for OmniFocus to finish loading your data in the background. But it's important to be realistic about how much faster it's possible for OmniFocus to be.
P.S. — I also realize that if the phone is asleep in your hand it will take even longer to unlock it before launching OmniFocus, and that if you left the phone running another app it could take even longer as you switch to the home screen—but those delays are common to launching all iPhone apps and I'm afraid that it's not something we have any control over. If you'd like to see the ability to launch third-party apps by double-clicking on the home button, please
submit your iPhone feedback to Apple! (Hopefully Apple counts votes for requests like that, as we do for our apps.)