> If you can show you can prioritize business value then it is easier to convince management

If your management needs 'convincing' then there's a problem.

Either the manager is technical enough to know whether a particular set of work is the right thing to do or not, in which case they don't need convincing. Or they're not, in which case they should defer to the engineer and also not need convincing.

The only managers who need 'convincing' on technical matters are technically inept individuals who nonetheless attempt to micromanage technical decision making. They are no more able to link business value to technical decisions than the engineers you say you distrust. Fire them.