Conjugate secondary antibody
Making an antibody-enzyme conjugate isn't trivial. By using a primary/secondary set-up you can use the same well-characterised conjugate in combination with many different primary antibodies (as long as these primaries are all raised in the same species). There is also the possibility of some amplification: for example, if the secondary is an anti-Fab then two secondary Igs will bind to each primary.

Response to OP comment

Most primary antibodies in common use are derived from rabbit or mouse, and most are IgG. So, for example, the secondary antibodies goat anti-rabbit IgG and goat anti-mouse IgG will cover most experiments.