Radio receiver: RF Gain vs IF Gain vs IF Filter stages vs AF Gain?

[TimFox]

More voltage = more pleasant sounds. get it now?

No, it doesn't works that way.

If you want higher sound volume, it needs higher power. The transformer cannot increase power. You're needs active circuit for that - power amplifier.

For the 5th time maybe? a current amplifier increases power. You get the voltage gain from the transformer, get the power gain from the IF drive stages.
Instead of getting the voltage gain from the drive stages, you get the voltage gain in the IF transformer, with a higher ratio.

If you use a BJT with an HFE of 100 as an emitter follower, the current gain will be 100, the voltage gain will be 1 - 1/100.
The resulting power gain will be 99
Which is slightly more than 1

Useful generalization and elementary (approximate) description of the three amplifier topologies:
("Unity" is approximate in the first two cases.)

Common-(base, grid, gate) amplifier:  unity current gain and normal voltage gain, therefore moderate power gain.
Common-(collector, plate, drain) amplifier:  unity voltage gain and normal current gain, therefore moderate power gain.
Common-(emitter, cathode, source) amplifier:  normal voltage gain and normal current gain, therefore higher power gain.