Since there are often multiple answers to quadratic equations. That is the important thing to remember in mathematics, I think.
‘The square root” implies something singular and refers to the positive, principal square root. That is more semantic and personally, I think less important practically.
There are situations in which negative numbers do not make sense so it does make sense to only think of a positive value for the square root. But not all situations.
Personally, I would rather see two different symbols for square roots in general and for only finding the principal square root. I would like to see a new symbol for the square root finding the principal and have the usual symbol imply multiple solutions.
But I don’t get to decide these things.
Maybe the idea of a different symbol could catch on though.