In certain regions there was a time when wood siding was commonly installed over building paper with let-in diagonal bracing instead of sheathing boards or panels. Its still allowed by building codes so it isn't surprising to find it in an older house in LA.
What is surprising is that a contractor would not suggest adding panel sheathing.
If its not too late, I recommend adding Huber Zip system with no house wrap, but if its too late, good quality cedar siding installed well might last another 60 years. Detailing at modern nail-fin windows will be a little tricky.
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Like the vanity top and sinks. Not the faucets
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