OK, I install my TP rolls “backwards”. But I have a good reason.
I have a very small bathroom. Space is tight. The TP holder is built into the wall RIGHT next to the toilet. It’s really close. And I tend to buy the large mega rolls so I don’t have to change it daily. If the paper rolls out from over the top, it is actually at risk of unrolling INTO the toilet. It’s just too close for comfort, so I install it the other way.
Another reason for over-the-top as opposed to under-the-bottom:
These days virtually all toilet paper is white (except for the light tan unbleached recycled stuff my employer also sells) but there was a time, long long ago, when patterned toilet paper was a bit of a fad. And the patterned toilet paper was designed to display said pattern when installed over-the-top.
Though really, considering what one does with said paper, I’m not sure it really matters in the end.
I also remember toilet paper that was in neon colors, back in the 1970s. In addition to some people having embarrassing skin reactions to the dye, said dye also interfered with septic tank bacteria, and that’s why it’s hard to find, except as a novelty item.
Whether you roll it from the front or back, squashing a roll before putting it on the spindle will usually slow down a curious child or pet. (Usually.)
My mom had one of those weird toilet paper dolls. She only used it for a spare roll, not the active roll, so it wasn’t as bad as it could have been (handling the doll while wiping??). But I still thought it was creepy as hell to have that doll sitting in the bathroom watching me poop.
Holy sh*t! One of my grandma made those back in the day. She also crocheted covers shaped like turtles for bars of soap (the extra bar that sat out waiting for the currently being used bar to be used up).
The TP holder in my new house is installed in such a way that when trying to twist around and reach it, I inevitably knocked it off the holder and it would immediately roll in a random direction to a spot that I couldn’t reach.
Given that there didn’t seem to be any better place for it, I got one of those freestanding TP trees. For some reason, it is easier to use with the paper coming off the back.
It’s this one if anybody wants to opine on why this might be.
Heh. In the end.
I’ve never once thought about which way the paper hangs.
But is the unexamined bog-roll worth wiping?
You’re a barbarian.
And, in my experience, neither cats nor children are deterred in the slightest by the distance from the toilet paper to the wall.
Nice. “Improper, overhand fashion.” So I guess I’m okay, even though my preference may be slight. 
I’d argue if you spend a lot of your time contemplating how you wipe your ass, that maybe it’s not much of a life in the first place.
Wait…What?
Not my fingers. Nope.
Well the OP asks us to justify our reason for hanging the roll correctly but not justifying his reason for hanging it bassackwards.
The reason one hangs it from underneath is the slight additional friction makes getting the amount of TP one wants much easier and natural. From over the top it can easily overspin, conserving resources and saving the planet, and perhaps some septic systems also. It was not due to us looking after cats ,but cats looking out for us and our best interest. They were were warning us of the consequences of this detrimental practice which throws humans out of harmony with the universe. Only humans who have not evolved to have their charkas resonate with the melody of the spheres hang their TP overhand, and suffer the universal karmic consequences.
I can see the potential wisdom in your argument for underneath TP mounting. However, the whole friction thing only makes any sense if you are a one-handed TP puller (e.g. you gently pull the necessary length of TP and then give a sudden and violent jerk to tear at the base of your pull, with one hand). I would hazard most civilized people will use two hands: one to pull the necessary length, and the other to hold the roll at a stop when it’s time to detach. No, do not stray from the True Path: TP must be pulled from the top (with exemptions for people with pets/small children). There is no other way.
Just hang your roll from the ceiling. Everyone’s happy, and it always looks like a party in the bathroom.
Ages ago one of the TV stations had a feature piece on the five most expensive hotel suites in San Francisco.* One of the managers said that he was giving a group a tour of the suite when two women broke off from the group, hustled over to the bathroom, and came back after only peering through the door. When he asked them what that was all about one replied, “We’ve been arguing about the proper way to install toilet paper and we figured you would know.”
*I forget where it was but the most expensive was $2,500 a night thirty years ago.
“Bog-roll”. Funny!
It’s on the dispenser roll. It could still sitting on the back of the toilet like it has been for the over two weeks since the last roll ran out. 
It tears off more easily when hung underneath. Also: Cats unspooling the whole roll.