Carrier systems make a six-aircraft flight deck uneconomic

Is a destroyer-sized carrier with six aircraft and two helicopters a workable solution?

No; it carries too few aircraft to justify the expensive systems and support infrastructure required for carrier operations.

A sustainable minimum carrier group is closer to eighteen aircraft than six or eight. Catapults, recovery equipment, maintenance spaces, aviation fuel, magazines, and control systems remain necessary even for a tiny embarked force. Many of those costs do not fall in proportion to aircraft numbers, and the same problem persists for V/STOL ships. The result is a great deal of specialized ship for only one or two useful flights of aircraft.