So, a little differently from other answers, I'd assume that eldritch abominations (EA, I like this abbreviation!) are:
- genuinely willing good to humanity,
- can reason logically, it's just humans fail to understand their logic,
- cannot do direct communication, as humans' heads explode if they do so.
This is a classical social Sci-Fi premise of "willing to do good" on lesser civilisations. The determinative questions now are:
How advanced over humanity are EA?
What can they do, humanity cannot?
In how bad shape is humanity in the opinion of EA?
How much sympathy and condolence does the view of humanity arise in EA?
There are multiple takes to answer these questions, the resulting options vary. I'll pick a single most interesting one.
A classical Russian Sci-Fi (ha, thought, I'd miss that?) "Hard to Be a God" takes somewhat a twist on that. Humans (advanced, space-faring, and communist) meet humans (in Dark Aged, bloodthirsty, bad) and try to help them. There is a classic dialogue, that I would like to translate and recite with insignificant cuts. It's the space guy, willing to help, speaking with a local scientist of Dark Ages, who thinks all the hope for local humanity is lost.
"If you could give god an advice, what would you do? What should an
allmighty do such that you could say afterwards: now the world is good
"Well. I'd tell him: I don't know your plans, maybe you did not indent
people to be kind and happy. Wish for this! It's so easy. Give them
enough food, enough clothes and shelter. Let famine and poverty
disappear, and also all what separates people."
"You think it is not enough?"
"The god answers that this would not help and would not be good to the
people. The strong ones of your kind would take what I gave to the
weak ones, and weak ones would still be poor."
"I'd ask the god to protect the weak, to influence the harsh rulers."
"Cruelty is power. The non-cruel rulers loose the power and other
cruel ones take their place."
"Punish the cruel ones. Make it offending to the strong to tyrant the
"Human is born weak. A strong one emerges when no one around is
stronger than he. When cruel of the strong are punished, their place
would be assumed by strongest of the weak. And they'd be also cruel.
Everyone would be punished, I do not desire this."
"You know better, oh allmighty. Do so that people obtain everything
and do not take from each other your gifts."
"This would not do good. When they receive everything for free from
me, they'll take it for granted. They will forget how to work, they'd
loose the interest for living and turn into my pets that I would need
to feed and clothe forever."
"Don't give then all at once. Give them slowly a little."
"Slowly people would also take themselves all they might need."
"I see it's not that easy. I did not think about such things
previously. But... The is a way. Make people love work and knowledge
most, to make work and research their single life goal!"
"I could do this, too. But should I strip the humanity of its history?
Should I fake one humanity with another? Would it not be the same as
to eradicate all humans from the planet and recreate new ones
"The, oh god, erase us from the earth and recreate us more complete...
Or even better: let us alone and let us pave our own ways."
"My heart is full of pity. I cannot do this."
I am not sure my translation was good enough, but this is one of the most powerful dialogues I ever read in Sci-Fi.
Back to EA! So, assume they are like 1k years of progress more advanced than we are. Also assume they think our current state of affairs is miserable (partially for a reason). Here also goes the initial assumption that they have a heart. They are good-willing for us. (Goodwilling in the way they think good themselves – we might not agree with them!)
Then they will feel the urge to to something to help us. They just cannot leave us alone, even if we ask them to. Because, precisely, their heart is full of pity towards us.
Of course that's one possibility of many.
Oh and about exploding heads? With technology advanced enough, they would be able to do whatever they want anyway without talking one-to-one. And it's the latter thing that causes all the insanity business, isn't it?
If any of their tech or indirect influences makes us go crazy, they might seriously consider to leave us alone. Because, even if they mean good and are willing to help, in this concrete setting they really cannot. So they just move on with a frail heart.