Why a warship cannot accelerate like a dragster

Can a warship be designed for exceptional acceleration over a short distance like a dragster?

Only to a point; increasing hydrodynamic resistance soon consumes the available power, and a large ship must also remain maneuverable.

A small speedboat optimized for straight-line acceleration is very different from a manoeuvrable warship. A large ship can keep accelerating while added power overcomes resistance. As speed rises, however, moving water aside and overcoming hull friction consume rapidly increasing energy. The water effectively changes from a flowing medium into a progressively harder barrier, so the available propulsion plant eventually cannot buy more speed.