What happens when you have no computer, no electricity, no phone etc.?
Secondly, it is good mathematics background to learn how the process works...good practice at algebraic manipulation.
I agree that there is no reason to do onerous calculations as a matter of course, but understanding how the process works IS important. There are many processes for which the computer is a great assistant and this may be one of them, but it is an ASSISTANT to your thinking and understanding, not a replacement for your thought process
And, of course, somebody has to know how to write the programs to do the process...and maybe someday the person is you!
That answer may not satisfy you until you have done enough mathematics to "get it"!