Why would you use an assignment in a condition?

The idiom is more useful when you're writing a while loop instead of an if statement. For an if statement, you can break it up as you describe. But without this construct, you would either have to repeat yourself:

c = getchar();
while (c != EOF) {
    // ...
    c = getchar();
}

or use a loop-and-a-half structure:

while (true) {
    c = getchar();
    if (c == EOF) break;
    // ...
}

I would usually prefer the loop-and-a-half form.