NoNonsense:
Of course there is a concept of Shoel Eitza. I do it all the time, with both my Rov and a close Rebbe of mine.
The difference is they know my personal situation, I try to give them as many details as possible, and they can give me an eitza that fits my personal circumstances.
On the other hand, asking a “Gadol” “what should I do?” without any background, without knowing your personality, and without any information regarding what the real issues might be is GIGO.
The other criteria is that both of these Rabbonim have told me numerous times “ask an expert”. If they don’t know, or think others would have better insight, they don’t try to hide it.
Is that “Da’as Torah”? Maybe. But it is not the normal usage in the Yeshiva World.