A thunderstorm that produces a tornado, winds of at least 58 mph (50 knots or ~93 km/h), and/or hail at least 1" in diameter. Structural wind damage may imply the occurrence of a severe thunderstorm. A thunderstorm wind equal to or greater than 40 mph (35 knots or ~64 km/h) and/or hail of at least ½" is defined as approaching severe.
4.2 How does the NWS define a severe thunderstorm?
A severe thunderstorm refers to a thunderstorm producing hail that is at least 1 inch in diameter or larger, and/or wind gusts of 58 mph or greater, and/or a tornado. Although lightning can be deadly, the NWS doesn't use it to define a severe thunderstorm. If it did, every thunderstorm would be severe, by definition. Also, excessive rainfall may lead to deadly flash flooding, but heavy rain is not a severe criterion either. The flood threat is handled through a separate set of watches and warnings from your local NWS office.
Sources: A, B
Maybe systems should be named somewhat in line with the NWS’s designation for a severe thunderstorm, that is, when one-minute sustained winds reach 50 knots. Anything weaker than that can be covered by other means rather than official advisories. Additionally, I would stop naming subtropical systems, and instead treat those as equivalent to nor’easters in practice. Therefore, my proposed definition of a tropical cyclone would be a purely warm-core, organised system whose sustained, one-minute winds reach at least 50 knots. Weaker systems would essentially be treated as equivalent to severe thunderstorms.