I feel like one thing needs to be considered here.
Stealth champions.
Stealth champions generally excel at getting around / to their targets unseen, and as we all know, pink wards are a direct counter to that.
Let's take a look at some of the stealth champions in this game:

You may notice I have left out
from that list. I only did that because their stealth is either Not played around as part of their primary combo (leblanc) or doesn't involve motion so the odds of being on a pink ward unknowingly are quite slim (teemo)
Now champions that are directly countered by pink wards:

Ok so what is the big deal right, some champions are countered by pinks and I want to counter them late game..
Well here is the thing... Most stealth champs that are shut down by pinks are ALSO given trouble by teams that group.
So what happens late game, when people run out of space for pinks? THEY JUST SO HAPPEN TO BE GROUPING AT THE SAME TIME.
Here is why we don't want pink wards to exist in the middle of lategame teamfights:
: Relies on her shroud for survivability, despite her sustain, she needs this to function in teamfights unless SUPER ahead.
: Already sucks enough as it is pls no more nerferino
: Relies on his ultimate invisibility to buy time for his Q and for repositioning before level 11 (based on popular evolution order). Post-11, Kha can rely on his reset mechanic for maneuverability but since he doesn't paint as many targets with damage as someone like katarina, he needs a fallback plan for getting around (handily enough, the stealth is less effective as mobility than the jump so it seems well designed as a fallback plan). Kha'Zix already falls off hard enough in the super lategame that removing his survivability via stealth would be very harsh.
: Relies completely and entirely on the element of suprise. Sure his burst is incredible, but he can USUALLY only eliminate one MAYBE 2 (if lucky), threats from the enemy team before being taken down or forced to back out. Does not do well if forced to jump into clusters unless SUPER ahead, or given opportunities via enemy mistakes.
: Relies on his Q stealth for initiation, escape, repositioning. Is already in a moderate place in terms of power with the current state of pinks. Improved Crit itemization recently helped him. (phantom dancer especially).
: Ultimate stealth is important to either getting in or getting out, already struggles in group settings.
: as much as i hate to say it, lategame pinks would hurt teemo too much, his ability to keep shroom cover is already gated by moving sweepers.
: wouldn't be hurt too much by this in the lategame I don't think. In a group setting, he already tends to use his stealth for the attack speed buff in combo with his ultimate.
For almost the exact same reasons as Kha, vayne needs her invisibility to function in super lategame due to her short range nature.
: initiation / escape you heard the spiel before :P
Look, I get why you would want this, however I hope that if you read this, you can see how this lategame lack of space for pinks is an intentional balance choice.