In so far as major browser support and working as advertised, then yes CSP nonce is suitable for production use. For cases where business reasons prevent changes to the website then it is still superior to not having a CSP or one that allows all unsafe-inline sources.
However as you hint at, using inline sources should be avoided where possible and nonces are meant as one way to work around the problem. The CSP specification even goes to note:
Using a nonce to whitelist inline script or style is less secure than not using a nonce, as nonces override the restrictions in the directive in which they are present. An attacker who can gain access to the nonce can execute whatever script they like, whenever they like. That said, nonces provide a substantial improvement over 'unsafe-inline' when layering a content security policy on top of old code. When considering 'unsafe-inline', authors are encouraged to consider nonces (or hashes) instead.
One of the biggest security benefits of CSP is exactly to prevent the running of inline scripts and inline styles. Hence the nonce and hash solutions should only be used if you really have no other choice.