That is the general idea. That area isn't terribly complex. It's a single layer with a caged nut on the backside of it. I'd remove a rectangle with the striker assembly still attached, take it apart on a bench (nut, cage and sheet metal part) then build the replacement piece. You can re-use the nut and cage obviously...
I would treat it like a drywall patch too, using backing around the perimeter so you can put some heat into it without blowing through, or ending up with weak and thin areas. Then when you have it all patched make sure your door is adjusted properly, and engages the striker correctly. A lot of the problem with fatigue in this area begins with doors not set right and the striker bolt taking a beating. It's not there to help lift and center the door, it's just there for the rotary latch claw to engage.