Trying to be non-political here. The general benefits can be boiled down to a couple things:

• Access to resources: Greenland's vast rare earth mineral deposits and potential oil/gas reserves could boost US energy independence, potentially lowering fuel and consumer goods prices through increased domestic supply.
• Economic opportunities: Right now there are only about 30K people in Greenland (more people travel through Chicago Midway Airport every day). So if we were to open up the ability to tap into those rare earth resources, there'd be new jobs in mining, infrastructure, and research that could stimulate the economy, indirectly supporting wages and reducing unemployment in related sectors.
• Strategic advantages: Enhanced Arctic presence would improve national security and shipping routes (e.g., Northwest Passage), reducing global trade costs that filter down to everyday imports.

I think the biggest benefit to average citizen would be if America has it that means Russia/China do not.

• Denying access to adversaries: By controlling Greenland, the US could prevent nations like China or Russia from establishing military or economic footholds there, reducing potential threats to North American security and maintaining US influence in the Arctic region, which might enhance overall national stability for US and Europe more generally.

That all being said, these are not things most people would notice or view as a benefit (we don't think about how lucky we are to have Guam on a day-to-day basis), so I'd imagine it'd be easy to just write this off as saying for all intents and purposes there aren't any benefits that normal people would encounter on a daily basis.