Question: Would you use a statistical inference method that is correct only 50% of the time?

My answer: What sort of inference and what do you mean by “correct”?

For example, in linear regression, it’s not at all clear what “correct 50% of the time” would mean.

For some classification problems, usually “% correct” is not a good metric. You want to look at sensitivity and specificity and other measures.

For other classification problems, how good 50% is will depend on what you are predicting. If you are predicting, say, which state a person lives in of the 50 in the USA, then 50% would be very good indeed. If you are predicting if the person voted for Clinton or Trump, 50% is not good at all.