To illustrate the need for this feature, I attach four screenshots taken 
under the exact same conditions.

- "vanilla.png" is what a user would see without changing any default 
(after pressing TAB to display the completion candidates): the prompt, 
their input, and completion candidates in a *Completions* buffer above the 
minibuffer

- "master-icomplete-vertical-after-tab.png" is what a user would see with 
icomplete-mode activated and (setq icomplete-separator "\n") after having 
completed the last directory name with a TAB: the prompt and their input 
is completely hidden

- "master-icomplete-vertical-after-tab-tab.png" is what a user would see 
after pressing TAB a second time; note the "ng/" before point, which was 
hidden after pressing TAB for the first time and is now visible again

- "patched-icomplete-vertical.png" is what a user would see with the 
proposed patch