You can have great integrated instruction without any hood work. After all, integrated instruction involves both inside and outside reference. Where is the outside reference during hood work?
I am speaking genarically; in the usual case.
Integrated does not necessarily mean actually putting on the hood.
Each student is different, and needs different methods of training. There is no "one size fits all" approach to flight training.
If the student is truly capable of integrating his/her instrument references to his/her outside references, then there is no real 'need' to put the hood on...but why not? You hafta do it for 3 hours anyway. Why not get a couple tenths before solo?
But that's not my point. The need for putting the hood on in soon after a maneuver is introduced with visual outside and inside references is to give the student 5-10 minutes of time devoted to purely looking and studying the instrument indications as they occur. If he is only glancing at the instrument 20% of the time, he/she will not (usually) see the subtle changes that occur and learn to apply smooth control pressures as they change.
Looking inside after the change and reacting too late is not good training.
As Midlife said, some students tend to look inside too much, and this is handled by covering up the panel for a while to force looking outside.
This tendency to look inside too much might be cured by giving the student sufficient time inside, so that he will see what he needs to see, then force the looking strictly outside until he/she learns the proper balance. But the balance will never be attained if you initially force outside looking only.
It is a delicate balance that the flight instructor must find for that particular student.
Like rudder/aileron coordination. The goal is to teach the student proper coordination of both, but I know from experience that most students will try to 'drive' the wheel, just like their car, so I tell them this in the beginning, and tell them to lead with the rudder. At first that produces a skidding turn, but eventually becomes well coordinated, as the new student learns rudder pressure feel and aileron feel.
The same principle applies to learning the subtle movements of heading, altimeter, and VSI. You focus specifically on each one with it's own characteristics and control pressures to bring it under control. You are simplfying it for the student. One thing at a time until he/she is able to correlate and apply them in concert.