The mole is used extensively in chemistry, why not elsewhere?
Because the mole is not a convenient basis for people and TV sets (for instance, one mole of people would be approximately 86 trillion (short-scale) times the population of earth, or put another way the earth contains a human population concentration of approximately 12 femtomoles/planet), and because there's no connection back to atomic mass, which is what makes the mole useful in the first place.

This was not part of your original question, but addresses Manishearth's modifications:

Because atoms and molecules react in discrete units (cf. the law of definite proportions), the number of particles is more fundamental than the masses of those particles. The mole is useful in chemistry because it is defined such that the mass of Avogadro's number of particles (atoms or molecules) of a substance (the molar mass) is equal to the sum of the numerical values of the atomic masses of its constituent elements. The value of the mole is calibrated such that the molar mass of carbon-12 is exactly 12 grams per mole. On the periodic table you will note that the atomic masses given are non-integral (often markedly so, e.g. chlorine at 35.45 g/mol). This is because the atomic masses represent a weighted average of isotopic masses, and because the proton and neutron masses aren't quite equal.

The mole makes stoichiometric calculations particularly convenient as we can measure out, for instance, 16 grams (one mole) of $\ce{^{16}O}$ and 2 grams (two moles) of $\ce{^1H}$ and obtain one mole of $\ce{H2O}$. In the case of water, oxygen makes up 89% of the molecule by mass, but is only one of the three atoms present in the molecule. The mole is necessary to transpose stoichiometries involving single atoms and molecules (with their tiny masses) into the everyday world of grams and litres.