I appreciate that the tricky part of this would be what happens when a parameter linked to an auto complete field changes, but the extra functionality of the feature would make any workarounds for that issue more than worthwhile (for me just revert the auto complete field back to an empty field if the linked parameter changes would work).
I have a number of reports that use popup parameters that contain hundreds of options, and while a sort of shortcut is available on desktop reports (type first letter of parameter) these same reports on mobiles are an absolute nightmare to use with constant scrolling.