I think that could well be a good move, but as you say would really be an experiment that would likely cost quite a bit to code and test. Maybe a layer 2 implementation of this in the layer 2 reward pools might be more manageable. In general I see layer 2 spaces as an opportunity for experimentation and want to see the cost of entry to them lowered as much as possible. If the cost is lowered close to zero then they can literally be test spaces for changes to the user experience of layer 1, among other things.
I expect that in the coming year I will be working on customising more than one layer 2 token, so I'll be exploring the options for expansion/change - at the moment I don't really know what is and isn't possible.