The Functions sidebar (Ctrl + Alt + 5) should be searchable, i.e. when it is opened, a textbox should allow filtering the available functions.
This way, the following workflow would be available:
1) Ctrl + Alt + 5 to show the sidebar; the search textbox receives focus and is ready to receive text
2) The user types the parts of the formula to search what they want (search should consider the entire function name)
3) Arrow keys up/down can be used to select the formula
4) Enter will add the formula to the selected cell
Note that currently, as soon as the Functions sidebar is shown, it is neither possible to (i) type letters to move to a function or (ii) use the up/down arrow keys to navigate the list of available functions.
BTW the search would work similarly to how the Function Wizard works (Insert - Function).
I refocused the summary so this does not sound like an exact duplicate of bug 122718, which it now depends on.
I think the workflow you describe does make sense, and wouldn't be inconsistent with other decks: the Gallery and Navigator decks can get text input as soon as they are focused.
Even if bug 122718 is not implemented yet, the focus could be moved to the function list instead of the Insert Function button, as an interim solution.
With your implementation in bug 122718, you workflow works exactly as described. Please go ahead and close this one as fixed too! :)