I don't know if it would be difficult to code, but I do like the search bar for heroes on the Champion Select screen. If there was something similar in the shop it would be awesome, since it would save a few trivial seconds clicking through tabs on the menu and scrolling to find the appropriate item, or (as the streamers seem to do) clicking on a suggested item, picking a component, and then tracking forward to a different item it makes up.

I really think it would be useful, instead of clicking to open sub-folders and scrolling down an item list to find what you want, or going through a convoluted family tree of items.