Yes, it is necessary. It is my opinion that everyone should have some basic understanding of the math and physics that defines the world around them. It is my hope that natural curiosity would drive people to seek out this understanding. Algebra is of course (imho) a big part of this understanding.
Building along the same line that Karthik started: I recommend everyone read "A Mathematician's Lament" by Paul Lockhart (sometimes just referred to as Lockhart's Lament).
http://www.maa.org/devlin/LockhartsLament.pdf
-John