By default, "simplify" only performs one simplification step, and that is why some expressions, like the one in the question, are not fully reduced. However, you can get a better answer by forcing "simplify" to perform more steps:
In your example, I began getting the right answer after raising "Steps" to 15:
syms x
y = sqrt(1-sin(x)^2)
y = simplify(y,'Steps',15);
Now the output of "simplify" is "abs(cos(x))" as expected.
