What is the use case of noop [:] in bash?

You would use : to supply a command that succeeds but doesn't do anything. In this example the "verbosity" command is turned off by default, by setting it to :. The 'v' option turns it on.

#!/bin/sh
# example
verbosity=:                         
while getopts v OPT ; do          
   case $OPT in                  
       v)        
           verbosity=/bin/realpath 
       ;;
       *)
           exit "Cancelled"
       ;;             
   esac                          
done                              

# `$verbosity` always succeeds by default, but does nothing.                              
for i in * ; do                   
  echo $i $($verbosity $i)         
done                              

$ example
   file

$ example -v
   file /home/me/file  

If you use set- e then || : is a great way to not exit the script if a failure happens (it explicitly makes it pass).

It's there more for historical reasons. The colon builtin : is exactly equivalent to true. It's traditional to use true when the return value is important, for example in an infinite loop:

while true; do
  echo 'Going on forever'
done

It's traditional to use : when the shell syntax requires a command but you have nothing to do.

while keep_waiting; do
  : # busy-wait
done

The : builtin dates all the way back to the Thompson shell, it was present in Unix v6. : was a label indicator for the Thompson shell's goto statement. The label could be any text, so : doubled up as a comment indicator (if there is no goto comment, then : comment is effectively a comment). The Bourne shell didn't have goto but kept :.

A common idiom that uses : is : ${var=VALUE}, which sets var to VALUE if it was unset and does nothing if var was already set. This construct only exists in the form of a variable substitution, and this variable substitution needs to be part of a command somehow: a no-op command serves nicely.

See also What purpose does the colon builtin serve?.

I use it for if statements when I comment out all the code. For example you have a test:

if [ "$foo" != "1" ]
then
    echo Success
fi

but you want to temporarily comment out everything contained within:

if [ "$foo" != "1" ]
then
    #echo Success
fi

Which causes bash to give a syntax error:

line 4: syntax error near unexpected token `fi'
line 4: `fi'

Bash can't have empty blocks (WTF). So you add a no-op:

if [ "$foo" != "1" ]
then
    #echo Success
    :
fi

or you can use the no-op to comment out the lines:

if [ "$foo" != "1" ]
then
    : echo Success
fi