How to fix the support item problem
Why not just make it so there can only be one support item per team? If someone else has bought the item aka the support then no one else can buy it.
If other lanes aren't meant to use it there is no reason to leave it as an option for other roles. Then you don't need to band aid fix it by having the item not produce gold unless you're near your ally or so on.
Already had a similar situation with smite and jungle items right?