At normal AM medium wave broadcast frequencies, a range of 20 meters is fairly easily accomplished with a 100 mW transmitter and a 3 meter long antenna as long as the antenna is properly matched to the transmitter. Proper matching is the key.
Because the antenna and the tank are connected in parallel to the transistor collector, the antenna will be inherently matched at whatever frequency the transmitter is tuned to. But that certainly doesn't mean that the circuit is optimum or the antenna is optimum. It merely means that for that particular circuit and that particular antenna, the antenna is carrying as much RF as it can at any given operating frequency.
And, there is another issue at play. At these frequencies, the antenna will have an extremely low radiation resistance, and at the same time a very high negative reactance. A 3 meter antenna will have a capacitance of about 50 pF while the radiation resistance is only a few milliohms. To get maximum range, you need to send as much RF current through the antenna as possible. The RF current is split between the antenna and the tank capacitor. The total tank capacitance is equal to the antenna capacitance in parallel with the variable capacitor. At resonance, maximum RF current passes through the total tank capacitance, but at the lowest resonant frequency, only 1/5 of the total RF current will flow in the antenna because the variable capacitor is set to its maximum value. At the highest frequency, the variable capacitor will be at minimum capacitance and considerably more RF current will go to the antenna. To maximize the range, the transmitter should be operated with the minimum amount of tank capacitance. Therefore, to operate more efficiently at lower frequencies, a larger value should be chosen for the inductor, so that the resonating capacitance can be reduced.
Of course, this causes other problems. Since the antenna is part of the tuned circuit, movement of the antenna, or moving objects near the antenna will cause detuning of the transmitter. And if the antenna capacitance contributes a larger fraction of the tank capacitance, the detuning effect will be worse. There's no free lunch. In this case, it's a trade-off between frequency stability and efficiency.