Thank you for the additional details.
The main idea is that the CheckBoxColumnMenu has its own data property, so if the Grid has paging it can show the same data as the one shown on the page.
As for the virtual scrolling, yes I can agree we can have the same option to scroll over the data on the menu. By design, this menu is for cases where the user has a couple of available options and can easily choose the desired one by having a full look over them.
As we understand that each application has its specific business logic, and every feature has its designed place I can suggest making a feature request for it, and based on the community interest we will plan ti accordingly:
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