ichkeria, I'm assuming, perhaps rashly, that people have calculators already out. Most of them seem to have phones in their hands 24/7. The one on my desktop comes up in half a second.
However, I was indeed talking about larger numbers - not multiplying pi by the distance to the moon necessarily, but sums like 11 x 16, where even if you know your tables you'll still take 30 seconds to multiply 11 x 8 and double the result in your head. I can do that, but no quicker than I can do it with a calculator. That's where the value of rote learning does appear - or, in my opinion, doesn't.
My own recollection is that rote learning of tables took ages, maybe a quarter of an hour every day or two. Whether that's cost-effective in terms of the time you'll save later in life is one question; another is whether it would be more useful to use that quarter-hour for something else, maths or otherwise.