It is not a problem that is retroactively fixable by other means than by what they are doing now.
They could take Android closed source and put a restrictive license on it demanding that timely updates as a condition of use. All that would achieve is that the large vendors will either stick with the old, still free to use, Android or start working on their own systems they would control again - Samsung's Tizen, Huawei is developing their own, etc. It doesn't take much to piss a large vendor like Samsung off sufficiently to jump ship. They aren't married to Android and have plenty of resources to pour into proprietary alternatives. Google doesn't have much leverage there.
The result would be only a market fragmentation, collapse of the app market and loss of market share for Google. That would benefit exactly nobody.
Phone vendors are not interested in system updates - that's a pure cost they don't want to pay, they would rather have you buy a new phone or at least not have to spend money and engineering time on preparing patches.