How to choose drywall repair technique
I doubt that a 4x4 hole that's fixed with mesh tape would be durable over the long haul (my limit is about an inch), but if it was somewhere that never gets any bumps or touching, then maybe it would be fine. (You're replacing something that's 1/2" thick with something that's much thinner...)

On a practical level, you're apt to have problems with the mesh sagging/bulging. If you're brave enough to try this repair, I'd suggest you use a stiff mix of setting compound both to butter the edges of the hole and to do the first coat. Try and press as much through the mesh as possible. (I know that "stiff mix" and "press through" are somewhat incompatible.) You might also look into the 6" wide rolls of mesh tape. They'd certainly have more structure than 3 strips of normal mesh.