Why aren't airplanes like golf balls?

This is a very good question! Drag due to viscous effects can be broken down into 2 components:

$$D = D_f + D_p$$

where $D$ is the total drag due to viscous effects, $D_f$ is the drag due to skin friction, and $D_p$ is the drag due to separation (pressure drag).

The equation above demonstrates one of the classic compromises of aerodynamics. As you mention, laminar boundary layers reduce the skin friction drag but are more prone to flow separation. Turbulent boundary layers have higher skin friction but resist flow separation.

$$D \quad\quad\quad=\quad\quad\quad D_f \quad \quad\quad+ \quad\quad \quad D_p\quad\quad\quad\quad\quad$$ $$\quad\quad\text{less for laminar}\quad\quad\text{more for laminar}$$ $$\quad\quad\text{more for turbulent}\quad\quad\text{less for turbulent}$$

Generally speaking the more "blunt" the body is (such as a golf ball) the more likely adding dimples to trip the boundary layer will reduce drag. Airplane wings are less prone to separation since they aren't as "blunt" and as a result skin-friction drag is more important.

For more information see Section 4.21 of Introduction to Flight by John D. Anderson

EDIT:

Laminar and turbulent boundary layers are fundamentally different in many ways but the important aspect for flow separation is how "full" the profile is. The figure below is a schematic comparing the mean velocity profile of a turbulent boundary layer to that of a laminar one. $V$ is the velocity tangent to the surface and $\eta$ is the distance away from the surface. As you can see, for turbulent boundary layers, the fluid close to the wall is moving faster than for the laminar profile.

What causes the flow to separate is an adverse pressure gradient, or $dp/dx < 0$ where $x$ is the coordinate along the surface. Generally fluid moves from high to low pressure. In the case of a boundary layer that is on the verge of separating, the flow is locally going from low to high pressure. The figure below illustrates the effect this has on the boundary layer. When the flow near the wall begins to reverse, the flow is beginning to separate. Because the fluid in a turbulent boundary layer near the surface is moving faster, a turbulent boundary layer is better able to resist an adverse pressure gradient than a laminar boundary layer.

Most objects that are designed with aerodynamics in mind are slender. This is done specifically to reduce the adverse pressure gradient ($dp/dx$) over the surface of the object and reduce the possibility of flow separation.

Figures are from Fundamentals of Aerodynamics by John D. Anderson.

This might be a simpler version of the answers above. Total drag is a sum of the surface friction drag and the form drag (pressure drag). About 90% of the drag of a smooth sphere shape is pressure drag and the rest is friction drag. Putting dimples on surface will increase the friction drag but will reduce the pressure drag by having the turbulent boundary layer attached farther before separation. Thus the loss by the frication increase is minimal compared to the gain by the pressure drag decrease. In airfoil shape case, the friction drag is about 90% of the total drag due to already optimized form drag. Adding dimples on such shape will only increase the total drag.