The reason there is no need for an AD Zhonya's is because AD is used for consistent damage, not burst damage.
Yes, I'm aware some AD champions can burst, but most AD champions pump out consistent damage. It doesn't matter whether it's a marksman or a melee carry or a bruiser, they still do consistent damage over burst. Because of this, a Zhonya active is not as useful on AD champions as it is on AP champions, and for the few AD champions that would want a Zhonya active, it's extremely overpowered to the point that they would be banned every match.
Talon, Zed, and Kha'zix come to mind immediately as the champions that would abuse an AD Zhonya. It's only these three champions, because they're the only AD champions that favor burst over consistent damage. Once given one, they would be unstoppable. The only reason they don't use the current AP Zhonya just for the active is because they benefit more from Bloodthirster and Black Cleaver. They would buy it every game and make the must ban every game list. Riot would start nerfing them, but they would remain overpowered until they were gutted and made unplayable.
However, an AP Mercurial Scimitar wouldn't do this. It would definitely make Akali and Fizz stronger, because they could clear a CC and keep going. Katarina would be mostly unaffected because her ult would still be interrupted when it landed. However, already-appropriate nerfs to Akali and Fizz would bring them back in line after the item's introduction. They would need harder nerfs than without it, but they could be nerfed without being made unplayable because of the item's existence.
And FYI, many of those items do have "mirrors" in a way.
Rabadon's Deathcap and Infinity Edge are mirrors of each other. Both items provide multiplicative bonuses to their respective high-damage champions.
WotA used to have an AD mirror. It was called Stark's Fervor. It was removed because it was useless and never used, and reworked into the current Zeke's Herald.
An AP Atma's I oppose, because Singed is a thing. Also Ryze is a thing. I think an AD RoA could be acceptable though.
