If either proving or disproving a thing changes ABSOLUTELY NOTHING about your existence and provides you no beneficial knowledge or ability, then I would dare say that the thing either never existed in the first place, or it may as well not be in existence. In other words - it is as if the thing doesn't exist if it can be proved or disproved without gain.
As an example, take a murder investigation. Let's say we find out the actual truth about the matter. Nothing in reality fundamentally changes, however the beneficial knowledge we now have is that the murderer is a dangerous person that we need to keep away from others, which then does result in a change to reality. Whenever we "prove" something to a sufficient degree in reality, then we learn that we can ultimately rely on that thing - and it will always react the way we have proved it will. That is fantastically beneficial! If proving God's existence does not, in any way, result in a greater understanding of anything, or the ability to rely on something about God, and doesn't even provide us the knowledge that there is an afterlife, that we will be judged by God, what the criteria is, etc. - if it is true what YOU said - that proving God gains a person NOTHING... then it is truly as if He does not exist, and I would argue that there would be absolutely no impetus to live life as if He does.