There is here misunderstanding and it is difficult.
A true receiver (for wireless QAM) needs first to have clock recovery circuit to lock to Tx clock and this is a nightmare.
Once clock is recovered then other things are clocked by this pace maker.
The carrier tracking at Rx needs to lock to both rf frequency and phase. You may know the nominal Tx frequency centre but due to oscillator jitter and shift at both ends (and any mobile Rx) it will have to follow it. The phase must also lock at least in one qaudrant terms(1 of 4 quadrants for a cycle). It is no good locking to same freq but a changing or tilted phase.
The difficulty here is to understand these two concepts (freq and phase). If you can control phase of two different freqs you control both. freq and phase. If you control freq only you control freq ONLY.
some designs control either or both.
Your 1st design requires somebody else to control freq (apparently as we couldn't see any useful sense of error to be useful to push signal to baseband) but if given two inputs at same freq centre then it does give enough error to lock to one quadrant of cycle.
To test it keep rf and nco freqs at .1 then change the phase rf and see error.