He went out after he put his coat on.
Here we have a sequence of two events, both in the past. The preposition "after" makes the order of the sequence quite obvious.
He went out after he had put his coat on.
There is a sequence here, but it is not directly a sequence of events. The construction "went" expresses an action, but the construction "had put" expresses a resultative state which attaches to the agent. The action of the verb to put exists in this sentence only as an implication (or perhaps entailment) one inferential step beyond what is directly expressed.
If I have put my coat on (in the present perfect), it must be that I put my coat on (in the past indefinite) to attain that state.
The former example isn't a simplification of the latter. If anything, the latter is a complication of the former. Without further context, I can see no reason to evoke the resultative state. The direct sequence of actions is clear and sensible.
The same reasoning can be applied here, although the conclusion might be different:
He was arrested because he murdered his neighbor.
Again, we have a sequence of events. The preposition "because" makes the order of the sequence obvious. An effect cannot logically precede its cause.
He was arrested because he had murdered his neighbor.
Just as before, the perfect aspect is appropriate when the state of the agent is more relevant than the action. The sequence of events remains the same. The action is entailed and must precede the state which it produces in the agent. So, does the action or the state have more relevance?
He was arrested because he is a murderer.
This version of the sentence doesn't even use the verb to murder. The subject's state is the only thing expressed here, and it's expressed with the copula and a common noun in the subordinate clause .
In all three versions, it is obvious that the action of murdering was in the past at the time of the arrest -- even in the absence of the verb to murder. In the last version, the subject's state must have relevance since it is the only thing directly expressed.
"Tense simplification" is itself an over-simplification. The subordinate clauses "because he murdered his neighbor" and "because he had murdered his neighbor" carry very similar semantics, but they are subtly distinct. In this case, without further context, I see no clear reason to prefer one over the other.
I do see reason to claim that all three versions are clear, natural, well-formed, grammatically sound and quite sensible utterances. None of them obscure the proper order of events.