Although Algebra doesn't have an abundance of practical application, it's 'use' is an extremely useful way of teaching people to think, and solve problems. Also, algebra isn't necessarily 'x+y' and all that jazz, rather a way of solving problems by way of 'cancellation'. That's literally what the word 'algebra' is derived from.
Without algebra we wouldn't have anything like modern mathematics, which underpins every single modern science. You can't understand statistics without algebra; physics would fall, chemistry would fall, biology would fall. In short, algebra is one of the lights that lightens the darkness of our ignorance. We'd probably still believe that Sun goes around the Earth. Literally.
Think of all the people you know who have jobs. How many of them need anything past fifth grade math? Probably not many, am I right? Yes, algebra is important for science, but outside of those fields it is not needed too often. People seem to be getting along fine without using it on a day to day basis.