God says that if He at once stopped performing His prescribed duties, the whole world would follow his path. Does that mean if most of the people in the world deviate from their duties, God is also somewhere or the other responsible? That means He too is neglecting His duties although He Himself says that He need not perform any task?
I think the implications of your reference to The Gita are not correct. Lord Krishna, in fact, states in The Gita that He (and all who are wise) should continue to perform right action because lesser beings will always follow the example of the wise. Krishna encourages seekers and yogis to perform dutiful action, not only for its own sake but for the sake of the example given to others. He is not suggesting that either God or his devotees cease performance of rightful duties! (That doesn’t even make common sense, does it?)
It is certainly true and Krishna states it to be so, that should the Lord cease actionless action, creation would dissolve. This is not intended to suggest that He will cease or that we should do so. Indeed, one of the core precepts of The Gita is the necessity to engage in right action (the battle of life, so to speak). The Gita teaches all to partake in rightful action and duties, but without attachment to the results. (nishkam karma) We should act as instruments of divine consciousness and power, not as separate egos.
I think therefore, that the interpretation you are referencing is not the intended meaning. We must deal with reality as we find it. Then only can our vision grow to see reality as it really is! Ultimately, we are not the Doer. God alone upholds the creation and hides Himself in the maya (the illusion) of separateness. Our sole duty in life is to unmask the unseen Hand behind all being and doing!
Blessings to you,
Seattle WA USA