The Problem I see with Bot Mages.
I'll start straight up by saying I am not an ADC main, but im starting to understand you because Mages are indeed starting to become frustrating even for me as a Midlaner, but at least I have counterplay as a Diver/Assassin cuz i can get on top of them but ADCs have no chance and this is my conclusion:
Mana is no longer a resource in this game for mages. It only is a resource until Lost Chapter and Mana flow Band is stacked- And Lost chapter can be cheated with TP, which most mages in bot do. I have literally went in a practice tool and casted 43 spells as a lvl 11 Syndra with Torch+Cosmic before i got completely OOM (I could cast 2 ultimates in that window btw) which sends me to the 2nd point.
The lack of CDs. Everything just comes up super fast and with Transcendence + Lost Chapter item (Torch/Luden) you have close to full uptime as a mage. An assassin/Diver can punish that cooldown with insta gap close in lane yes, but what can the ADC do when the Mage spells outrange him and his gap close is inexistent.
Then there is the wave clear, every mage one shots waves from safety. ADCs nont named Sivir dont.
And finally is the kill threat. Most ADCs have no kill threat on Mages because Mages can fish or posture for burst dmg from outside of range of the ADC and back away if their fish was unsuccessful.
The ADCs selling point over the mage is exactly this: The lack of downtime as long as you are allowed to hit, but mages in modern League lack downtime, most have a defensive/peel tool that can be held, used aggressively or defensively (syndra e ziggs W, hwei fear,xerath E, Lux Q dont even get me on Mel W), but when CDs and mana costs arent there to gate them, their value goes through the roof.
Even against assassins and dive, they have access to Seeker/Zhonya which is not an ideal buy but its still better than ADCs' GAs
Finally is the counterpoint: Who is killing the Nasus/Ornn/Sion/Mundo if you have a mage bot. Well it wont be easy and sometimes it will be indeed impossible if your mid also picked Akali and so on but there is still the rest of your team and you likely put the enemy adc either so behind or in such an uninteravtive state (no kills, no plates) that The ADC itself wont be able to impact the teamfight.
Also the 6 item scenario, yes 6 item Cait outscales 6 item Ziggs as DPS, but she has to put so much mechanical and awarness effort, If she gets hit by an engage it is ziggs bomb in 1 ziggs Q and she dies. Ziggs just plays from a mile away and tosses Q at random hoping poke lands and if engaged on satchel Zhonya.
Tl&Dr: Mages mana costs and small downtimes along with their superior range and safe wave manipulation abilities power-creep adcs.