Security Weekly episode 436 had a section about password cracking that may be worth checking out if this is new terrain for you. About the effectiveness you can have lengthy discussions as recent hacks have shown. All the password policies are basically forcing people into making passwords in a smaller namespace then without strict password policies. Most passwors nowadays start with a capital character and end with one or more numbers that in most cases reflect the month or year.
And selling it to management depends on the organisation. Towards my current client is was easier to sell them better and earlier detection of (possible) abuse with easier unlocking and resetting of accounts, and adding two factor authentication for public facing services or services with high risk data/processes/accounts. Also a good automated joiners and leavers process reduced a lot risk.
Do we still do crack password? Yes, but mostly incidental during an audit. The main reason was that we assigned the money to other preventive measures as we couldn't check if passwords weren't reused outside of the company for example. We from "security and compliance" moved from the No-department to the department that enables the company to do their business safely and with reduced risks. This resulted in more productive hours and less interruptions for customers and users.
So find out how you can motivate your management as some want to have all the ticks they're required to have for the auditor/accountant and don't want to overpay. Others may be willing to take a risk and set some cash a side for it as long as they can make higher profits.
From a technical point of view it is great to get more awareness and to bring your organisation to a higher level.