I live where the median home is 900k and there is still no shortage of handymen and general contractor labor here if you are willing to pay for work under the table. It's an interesting dynamic.
It’s not an issue of how expensive houses is, it’s an issue of how many houses are being built. California has the slowest housing starts of any major state in the country. That same carpenter would have his pick of job sites in Florida.
Where in live in the US, the housing market is exploding. It is impossible to find these workers, licensed or not.