It might just be a mess to balance.
RoA have some hidden limitation for who can buy it. The said champion need to use all 3 of those stats. (Mana-less champion definitely do not want it.) Its not really that great initially, so that champion HAD to be able to make do while it charges or is very very effective with all 3 of those stat combine (Hi Ryze and Singed). It gives a decent amount of AP, but some of the gold value went to the tankyness it gives, the HP, which a lot of AP scaling mage do not care as much. (Extra hp is always nice, but you probably do not NEED it on burst mages) So overall it becomes a nice item to have while not making it a must for everyone.
Another thing if its scale with AD is, unlike AP, AD also effect your auto attack damage. Who would love more AD for scaling and auto attack damage? Your friendly neighborhood adc. So there is another layer of balancing to think about for this version of AD RoA.
If it only scale with tank stats, it might work. But usually at top lane if you are a brusier, you do not want to get a tank item first. Heck, even the "tank" champions want to get 1 offensive item first. (Hi Gnar) Very few champion only get tank item on first buy. So you probably have to get this on a second item or third item. THEN you have to wait for it to charge. I think we all see the timing issue with the item here. Also, additionally should it be an HP+Armor or HP+MagResis item? Or HP+Armor+MagResis? Since you do not always need the same damage type resistance. This becomes another issue of how many extra items to be made? More item means more balancing difficulties.
Then again, I agree, it probably would be nice to have an AD or tank version of RoA for the brusiers. I just do not see it can be easily done.
that scales with time, and I think it'd make a lot of bruisers happy as well, considering how outclasses they are in top lane right now. Something that gives a chunk of HP, some AD, and a third stat (preferably something like mana or AS so it doesn't become the go-to buy for every single fighter in the game).
