Why AC supply is rectified first before stepping voltage down?
The volume for a core, needed to support the Webers, is this:

$$ \left(volume = l_e\cdot A_c\right) \ge \frac{\mu_0\: \mu_r\: I_{peak}}{B_{max}^{\:2}} \int H\:~\textrm{d} B$$

\$l_e\$ is the required magnetic path length and \$A_c\$ is the core cross section area. In the case of a sine wave, the last factor above, for one half-cycle of applied voltage, is:

$$\int H\:~\textrm{d} B = V_0\int_0^{\frac{\pi}{\omega}} \textrm{sin}\left(\omega t\right) \:\textrm{d} t = \frac{2\: V_0}{\omega}=\frac{\sqrt{2}~ V_{RMS}}{\pi\: f}$$

For 60 Hz and \$V_{RMS}=120\:\textrm{V}\$, you get about \$0.9\:\textrm{V}\cdot\textrm{s}\$, which is huge.

Suppose I wanted \$10\:\textrm{W}\$. Then \$I_{peak}\approx 120\:\textrm{mA}\$. The flux density of iron cores probably shouldn't exceed about 1.5 Tesla (though we could look at various materials and come up with a range of numbers here.) \$\mu_r\approx 1000\$ for iron. So this suggests about \$60\:\textrm{cm}^3\$ of volume for the core -- or in the area of about 1 pound of weight. This is about twice the weight that is used as a rough guide for power transformers, but it is in the right ballpark. (Using another figure I've seen for CRGO steel, 1.9 Tesla, the weight drops down into the normal expectation range.)

Note that high permeability doesn't help you in the least. Look up at the equation above. That term, \$\mu_r\$, is in the numerator! If you increase it, all you do is increase the needed volume. The reason is that you need vacuum to store energy. Not matter. So more permeability simply means less effective vacuum space in the solid matter lattice and so you just need more matter in there. High permeability here is about containing the flux lines and providing good magnetic coupling. The inductance comes along for the ride, too.

Low frequencies just mean big volt-seconds and therefore big cores. Thus, "heavy iron." It just goes with the territory.