Why are tapped transformers needed in RF amplifier circuits?
Impedance conversion. 

Tapping the top of a tuned cct tends to load it, reducing its Q, broadening the bandwidth where you want a narrowband to reduce interference. In your first example the FET is a high resistance load but it still has input and Miller capacitances which you don't want across the tuned circuit. 

Tap at 1/3 of the inductor, and you transform the equivalent impedance across the whole tuned cct by 3^2 = 9.

Same in the 2nd cct : while the transistor approximates a current source, it adds a high but not infinite resistance across the coil : by connecting it to a tap, the impedance across tho whole coil is increased. (Also the transformer steps up the resulting voltage, increasing gain).

In the third circuit I suspect it's merely a way to get one of several step-up ratios (and impedance transformations) out of a standard transformer. I see part of a second one : was that connected differently?

Sometimes it can be used to convert from a standard impedance like 50 or 75 ohms from an antenna or transmission line to a higher one for tuning. 

"Impedance conversion" by adding resistors would add Johnson noise generated by the resistor : impedance conversion by transformer does not, as well as stepping up the voltage when an impedance increase is desired.