Why wasn't King David executed for his adultery with Bathsheba?

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Some people raise this issue in an attempt to claim that adultery is not a mandatory death penalty offense (contra God's law in Lev. 20:10). The claim is that, since David was not put to death for committing adultery, therefore it was considered acceptable by God to not require the death penalty for adultery. Here are three things to consider:

  1. First of all, this is an argument from silence (similar to the argument discussed in the Q/A: Does Joseph's intent to divorce Mary show that the death penalty for adultery was not mandatory?). Two eyewitnesses were required to testify before a judge in order to convict anyone of a capital crime. We do not know if there were any eyewitnesses to David and Bathsheba's adultery, and if there were, they may (for whatever reason) have refused to come forward. That is all we know, and we cannot draw any normative inferences from the lack of a civil trial in David's case.
  2. It is possible that God did not allow His explicitly anointed king to be held accountable by a human judicial system (only by God Himself). ("who can put out his hand against the YHWH’s anointed and be guiltless?" 1 Sam. 26:9) This would also explain the fact that Nathan -- God's messenger -- authoritatively proclaimed God's sentence on David's case (2 Sam. 12:13-14), which would obviously preclude any further (human) judgment.
  3. YHWH was probably determined to maintain his covenant with David (2 Sam.7:11-12), despite David's own sin, thus He punished him in indirect ways (e.g. death of his son). YHWH sometimes prioritizes covenant-keeping over other (temporal) aspects of His justice. For example, in the case of the Gibeonites. He (temporarily, not eternally) subordinates temporal judgement for the sake of maintaining a covenant.

What we do know is that God himself acted to bring a penalty against David, causing the death of his son: 2 Sam. 12:14-19. God could, as easily, have killed David and Bathsheba, but he obviously had future plans for them.