It's a good idea. But not sure if it’s that essential as it’s easy to do the same thing relatively quickly, manually.

Some things to consider :

1- Named filters (a way of memorizing filters settings, etc.) are on their way as a feature, so that you wouldn't have to research for the same things over and over, and manually write down your filters. You could have a grid with a recorded list of specific filters for different subjects-projects-contexts. I don't know when this feature will see the light though.

2- Like you suggested this is already easily achievable in 3 simple steps :

b- create your new grid (+ define its source if you're not going to use the IQ automatically created field for the new grid)

c- Drag & Drop all the items from the search grid to the new grid. Voilà. (If you have a complex source, there might be some issues -- which would be resolved by manually choosing which fields to assign to new items in the grid, in the grid management window --  but not if the source is simple, i.e. : a single field)

Keep in mind that creating too many grids might clog your grid menu. I do have many grids too, but it's probably not the best solution in the long term. "Named filters" will alleviate this problem, and also a better type and search functionality in the grid menu (which you can invoke with ctrl shift o -- then start typing, press enter when on the write menu entry... Note that there are 2 different ways of displaying the menu...).