Ad scaling item
What about an ad scaling item as the title says. Since ap affects tower damage there isn't really a reason anymore to not have an ad equivalent to roa. Maybe something that combines pick axe, fist and recurve bow. Have the total build cost be like 3100 or 3200. And have it scale up to 40% as, 800 health and 60 or 70 ad after 10 minutes (numbers are just a rough guess). Possibly tweaking cost or a unique passive if underpowered. Like switching out fist for kindle gem keeping build cost the same but have the cdr build to 20% after 10 minutes as well. I.e. Starting at 10% when the item is finished, at 5 minutes gives 15% cdr and at 10 minutes gives 20%. It could be an interesting item for the top lane or ad bruiser junglers like jV. Open to feedback or ideas about tweaking this further.
x Mana 
x game duration 
. Adding yet another multiplier (game duration) to the lategame potential of AD itemization is very likely to go overboard. I would argue that AD multiplicative itemization is already over-catered to and creates a lot of problems, such as making marksmen greatly outperform nearly any other lategame damage source to the point where they've been mandatory in almost every season since a marksman comp will usually beat a non-marksmen comp if they can just stall to the lategame. Only recently has that issue improved a little bit, with certain mages becoming a semi-viable marksman replacement, and I think this suggestion would be a step backwards...