It is my current view that the only right kind of influence is an influence beneficial to philosophy—“the world” be damned, if it weren’t for the fact that philosophy needs “the world” (I’m alluding to the last sentence of Nietzsche’s Genealogy, third treatise, section 7 here).
And his influence on philosophy is Plato’s true apology: for for the longest time, Platonism, Plato’s exoteric doctrine, was beneficial to philosophy… Nietzsche even says somewhere that the Church is a nobler institution than the State because it’s a hierarchy based on spirituality.
Only with the victory of Baconianism—i.e., of science over religion and its ostensible handmaid, philosophy—has Platonism truly become a threat to philosophy. And just as Plato rightly saw, back in his day, that his “noble lies” had become necessary for the sake of philosophy, so Nietzsche rightly saw that they had become detrimental to it.
But why would the only right kind of influence be an influence beneficial to philosophy?—Because only in philosophy does the object of human eros, i.e., of the human will to power, coincide with its true aim:
“We have been observing that, on Socrates’ account in the Republic, eros has a single aim but many objects. The case of the philosopher, though, reveals that we must amend that formula: however numerous its objects, eros as Socrates depicts it in the Republic has a limited number of proper or true objects, indeed, in the deepest sense just one true object. That object is the Good[.]” (Cooper, Eros in Plato, Rousseau, and Nietzsche, page 32.)
EDIT: This quote now reminds me of the following:
“The real community of man, in the midst of all the self-contradictory simulacra of community, is the community of those who seek the truth, of the potential knowers, that is, in principle of all men to the extent they desire to know. But in fact this includes only a few, the true friends, as Plato was to Aristotle at the very moment they were disagreeing about the nature of the good. Their common concern for the good linked them; their disagreement about it proved that they needed one another to understand it. They were absolutely one soul as they looked at the problem. This, according to Plato, is the only real friendship, the only real common good. It is here that the contact people so desperately seek is to be found. The other kinds of relatedness are only imperfect reflections of this one trying to be self-subsisting, gaining their only justification from their ultimate relation to this one. This is the meaning of the riddle of the improbable philosopher-kings. They have a real community that is exemplary for all other communities.” (Allan Bloom, The Closing of the American Mind, Conclusion.)
And cannot Plato and Aristotle be understood as a (spiritual) erastes and eromenos? Aristotle started out as a pupil of Plato’s, after all… Not to mention Socrates and Plato!