Most people who've commented about using Wolfram Alpha are just using just its Mathematica backend - calculations, plotting graphs etc. I found this pretty useful while trying to solve some algorithmic coding challenges which involved large numbers. Mathematica works with numbers larger than what either Python or Ruby can support.
But otherwise apart from the Math part, haven't heard any use case yet where the data analysis that Wolfram Alpha does was terribly useful.
I find it very useful when dealing with unit conversions and fundamental constants. Google is fine for simple stuff but Alpha really excels when you have extremely complicated combinations of units. This probably doesn't matter much outside of physics but within it Wolfram Alpha is a godsend.
Python integers have unlimited size. It’s true though that the support for fractions, numbers with whole multiples of π and e, square roots of arbitrary numbers, etc., is better in Mathematica/Maple than a general-purpose programming language.
But otherwise apart from the Math part, haven't heard any use case yet where the data analysis that Wolfram Alpha does was terribly useful.