You need to be able to perform long division to take quotients in algebraic structures, e.g. polynomials. Yes, Wolfram Alpha can probably do it, but not always.
You don't need to understand long division to be able to do that. Long division is over the integers. It's got a weird notation, and I never learnt it.
There isn't any reason for 99.9% of mathematicians - even in abstract algebra - to know long division.
