The reason there is no need for an AD Zhonya's is because AD is used for consistent damage, not burst damage.
[snippet about who would use AD Zhonya's]
You...do know you're talking to a person who has spent a lot of time micro-analyzing this game, right? An analogue would be explaining long multiplication to a college student.
And FYI, many of those items do have "mirrors" in a way.
No, they do not. They have items with similar goals, but they do not mirror each other.
A mirror would be Last Whisper/Void Staff or Archangel's Staff/Manamune.
Rabadon's Deathcap and Infinity Edge are mirrors of each other. Both items provide multiplicative bonuses to their respective high-damage champions.
No, they are not mirrors. They are mechanically and functionally different. They are based on the same job, a multiplicative increase in damage output, but they do it in mechanically different ways that mean different things for different champions.
If there were an AD Deathcap, then champions like Riven and Zed would get more effect from it than Infinity Edge.
If there were an AP Edge, it would benefit multi-hit spells and rapid spell combos like Ryze and Vel'koz (not saying Vel can't use Deathcap, but if his multi-tap spells could crit...)
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.
The current WotA--AP, CDR and Spell Vamp--does not have a mirror. It has similar corollaries, such as Essence Reaver, but they have different purposes and are built for different reasons.
The old WotA and the old Stark's Fervor both had one mirrored similarity: 20% of their respective sustain type. While WotA granted 30 AP and 20% SV to allies, Starks gave +20% AS and +20% LS to allies. WotA had no other effects than the base 50 AP and the aura; Stark's had a base +20% AS and 20 ArPen.
They were closer to mirrors for sure, but the differences made them useful in different contexts on different types of teams.
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.
Does no one remember Vladimir? The living AP Atma's that Riot really should rework at some point?
In any case, an AD RoA would be weird to balance. Most AD champions don't want sustain that only happens while they're leveling in the laning phase, but if it was strong enough, bruisers would probably have a 100% pick rate.
