re: The US economy gained 236,000 jobs in March

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But having wage growth still at 4.2% is still a bad sign for future inflation in my opinion.

Wage growth is an engine for future inflation. It burns hot and it burns for a long time. All business expenses wind up as an increase to the consumer. Which in turn spurs additional wage growth (employees have to actively look for higher paying jobs to pay the same bills. Inefficiencies in wage markets drive up wage income in certain sectors which drive up wage income in sectors that were originally operating efficiently).

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You are spot on with your analysis and unless we have an depression type event in the US there is no way for those wage inflation to get back into check other than rapid automation across all job sectors.