The phrase "in many industries" is correct and usable in written English. You can use this phrase when you want to refer to a concept or idea that is applicable or widespread in many different industries. For example: "In many industries, the demand for skilled labor is on the rise.".
It's bad in many industries.
Change is being made in many industries.
"In many industries, jobs are being cut.
Jobs in many industries are developing rapidly.
In practice labour in many industries is quite flexible already.
Sadly, in many industries these barriers remain in place today.
Conflicts of interest are inherent in many industries.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK