I don't know why both the question and some of the answers mention short-circuiting behavior of the corresponding logical operators as a potential issue.
There's absolutely no short-circuit-related problems with defining &&= and ||= operators. They should be defined uniformly with += and other similar operators, meaning that a &&= b should be equivalent to a = a && b, but with a being evaluated only once in &&= version. This means in turn that b is not evaluated at all if a is originally zero. Easy.
So, the only reason they don't exist in the language is, well, "just because".
