Cursive is where most OCR breaks. Connected letters remove the whitespace that printed-text engines rely on to find word boundaries, and letterforms like "rn" versus "m" or "cl" versus "d" become genuinely ambiguous. This is exactly the case general document OCR was not built for.
The tools that handle cursive well are the ones trained on real handwriting from the start. In our testing, specialist engines lead comfortably, LLM vision sits in the middle (helped by language priors, but prone to inventing plausible words), and the cloud document APIs trail on connected script.