True, and a very good example is the multiplex kits available for simultaneously detecting multiple anti-SARS-CoV-19 isotypes (e.g., IgG, IgA, IgM) in blood in response to infection or immunization.

Antibodies are pretty stable molecules but physically attaching any additional moiety, such as a fluorophore, risks creating steric hindrance issues and reducing antibody binding to it's target antigen sequence. Even the smallest modifications such as biotinylation can slightly reduce binding in some instances.

These physical access issues can be more important with '2D' systems when the target is immobilized on flat microtiter plate bottoms, which effectively hides the bottom side of the molecule from exposure and target binding to the ELISA plate can alter its physical structure presented to the antibody, compared to 3D exposure of target/detection antibody in liquid/suspended environments.

Also, secondary antibodies are great for signal amplification, but non-specific background binding goes up, too, versus using a labeled primary ab. This isn't really an issue if appropriate controls are included, and the signal amplification is proportionally greater than any increased background binding.