>= and <= for string comparison

[Peng Yu]

       string1 < string2
              True if string1 sorts before string2 lexicographically.

       string1 > string2
              True if string1 sorts after string2 lexicographically.

According to the manual, >= and <= are not available for string
comparison. But if >= and <= are available for arithmetic expression.
Why >= and <= can not be introduced for string comparison? Currently,
as a walkaround, I have to use > and = for >=, and < and = for <=. It
is rather cumbersome to write bash code in this way.

-- 
Regards,
Peng