Why there is no resistor in an AM Detector?
Perhaps you are misunderstanding the word 'detector', which is what rectifiers were called in the 'olden days'.

In your first circuit, the tuned circuit filters the incoming signal. The antenna has a finite impedance, it's not a voltage source, so allows the tuned circuit to suppress the response at higher and lower frequencies. 

Amplitude modulation is a way of transmitting a low frequency signal which is coded into the amplitude of an RF signal. Mid level RF signal means zero signal. Lower level RF means negative signal. Larger amplitude RF signal means positive signal. However, all this time, the RF signal is swinging positive and negative, with zero average.

D1 is shown without a load, but in reality it will be followed by a resistive load to ground. When the incoming RF signal is larger, the peaks of the RF signal will be rectified by D1 and produce a large current in its load. A small RF signal produces little current into the load. The changing load current represents the signal modulated onto the carrier.

In your second circuit, you have the tuned circuit behaviour, but no rectifier, no detector. For a big signal, the output swings a lot above and below ground, for zero average output. For a small signal, the output swings a little above and below ground, for zero average output. The average output then is always zero, regardless of the modulation. You have 'filtered' the carrier, but you have not 'detected' it.