And of course all of this is scriptable, so if you wanted to reset all of your existing due dates to a time which works better with your iOS device you could do that, and then change the default due date time to the preferred value under preferences.

[spiliog]

Great point whpalmer4 but my "request" is for an option to set or not a time/alert. Simple as that

[whpalmer4]

You initially asked if you can set a due date without setting an associated time. You can't. OmniFocus only presents an illusion of caring about dates, but really, everything is just some number of seconds after the beginning of time, and dates just make it easier for humans to specify which instant in time. If you restated your question as "is it possible to set a due date only setting the month without setting the day of the month?" you would have a comparable situation. What does it mean for an action to be due in August?

If you want the option of controlling alert behavior on an action-by-action basis, then ask for that. That makes a lot more sense than asking OmniFocus to invent new data types, which still wouldn't provide generally useful control of notifications.