During the collection of ideas, often end users don't know/want to think about which product it may sit within.
Also during Product Mgmt brainstorming of ideas that will come later, they could spark a cross product effort (especially when a Platform is involved!).
What we would like to see is the ability to enable/disable idea capture at various levels. For us and our platform level, we would like to enable the capture the ideas here and may (or may not) want to disable at one or more (child) products.
When promoting an idea to other stages in the roadmap, we would see us assigning a specific product who would then own further.