The “experiential problem of evil” isn’t simply emotional, and emotions should not be discounted anyway.
I agree that, even pragmatically, attempting to solve the problem of evil by positing that “you cannot prove that God doesn’t have sufficient reasons for doing it” still leaves a lot for a believer – or non-believer – to struggle with.
For one thing, it’s an argument from ignorance; it falls short of saying that you
know what God’s reasons are. Instead, it’s an admission that one is ignorant of what those reasons are, but that one knows that – logically speaking – those reasons could exist. In a very real, pragmatic and emotional sense, a believer’s relationship with God is going to be materially affected by the dynamic between instances where they can feel and appreciate God’s love – a miraculous saving of life; an answered prayer – and instances where the best they can do is say, “I believe God has a reason, even though I don’t comprehend what those reasons are” (e.g., a seemingly senseless tragedy).
I think it’s also true that what apologists gain in saying “you can’t prove that God doesn’t have sufficient reason for permitting what you call evil” is lost in its complete open-endedness. Anything and its contrary could exist in a world where God loves us. Jesus could never have come to this earth – and it would not, in itself, disprove that God loves you. There could be no plan of salvation – and this would proves nothing, because God may have had sufficient reasons for having no plan of salvation. There could be no immortality of the soul, no heaven for those who believe – and, again, this would prove nothing, would not prove that God doesn’t love us. Indeed, by the standards of slaying the problem of evil by saying, “God has sufficient reasons that you do not understand” even a statement such as “for God so loved the world, that he gave his only begotten son” itself becomes relativized, as it were; God could have
not given his only begotten son, and you still would not be able to prove anything against God, because you cannot presume to understand God’s ways. And, just as what you subjectively would call “the bad stuff” doesn’t prove anything against God, so would the “good stuff” not prove anything
for God, in and of itself. Your interpreting “bad things” as a sign that God doesn’t love you could be mistaken, but so too could your interpreting “good things” as a sign that God loves you be mistaken.