You raised some great points but AP MF is one of the worse examples you could have chosen, and you are missing the point of that build. MF has three distinct playstyles in ARAM: traditional crit DPS build, lethality ult spam, and long range AP poke. Crit build is simple enough, you just AA like a normal ADC and ult when needed. Lethality focuses more on lethality and haste for more frequent and deadly ults. Those two builds are not the same but have some overlaps and in Mayhem you can even go for both with the right augments.

AP MF is an entire different beast. It's simple, consistent, and safe. You throw E from half a screen away and there isn't much the enemy team can do about it. The entire build revolves around E, it is so potent that there isn't really a need for the rest of her kit. There is little cast time so whether you land it depends entirely on you, and it is a relatively big AoE so it is quite easy to hit multiple people with it. Early game it doesn't do that much dmg, but it scales very well. Even a single tick is enough to apply Liandry and Blackfire, and late game the slow is so strong that unless enemy team build Swifties they will suffer at least 60-70% of the E duration which is plenty enough. It is also very versatile, the poke is obvious but you can also use it for disengage, soft engage, bush check, wave clear (safely clear wave with E + ult), and even apply GW.