If you need to sit down and 'spit ball' 'blue sky' or 'workshop' your brand's purpose, then it isn't really a purpose, it's a marketing ploy.
The fad for 'Brand Purpose' seems to have usurped the much mocked 'Mission Statement' as this year's superficial marketing bunkum. The superb Tom Fishburne makes the case best in this cartoon. (See his other work here)
A brand's purpose should be obvious. If it isn't obvious, then it's unlikely the brand would even exist. Why would you buy something if you didn't know what it did? A washing powder's purpose is to clean clothes. A running shoe's purpose is to help you run faster. The other stuff - the saving the world stuff - is what a brand might support but it isn't its purpose.
'Consumer' brands might want to align with other brands or initiatives that have a purpose. A charity perhaps. They can even set up their own charity and direct some of their profits into that charity. But the idea that a washing powder's 'purpose' is to help underprivileged kids have a better life is absurd.
Let's stop this bullshit and get real.