1. For preserving randomness from independent sources, multiplication and division are rarely useful. These operations at times reduce randomness - take for example, the well known, multiplication by zero. Otherwise what was very good randomness, is destroyed. Even multiplication by a very small number takes away much of the randomness derived from other sources. If a Slashdot topic is not conducive to AC posting (or any posting at all), there goes all other randomness in the bin.

Similarly division - division by large numbers have similar effects as multiplication by small numbers.

XOR is typically better. But then one has to be careful that the "independent" sources have very low correlation - otherwise probability of zero bits increases drastically.

2. You need random, and you need it quick. The hunger of modern computer systems is difficult to satiate simply by the sources you suggest - at least initially. E.g., if you want to download all these figures from the internet, would you want to download such sensitive stuff in plaintext ? Of course not, you need SSL. For SSL, you need random. So you are stuck with good quality hardware RNG for best results, bad quality randomness without that, or depend on system entropy.

Once you get SSL, you could store lots of random numbers, but then you get into the problem of people / attack vectors trying to read that store. Performance vs. non-storage is a tough problem to solve.