Is there a practical use of streaming data received from meteorological sensors installed on aircraft?
Yes, such a system would be beneficial to pilots, ATC, and meteorologists.
Pilots are very concerned with meteorological phenomena like icing and turbulence (for safety-of-flight reasons) and winds aloft (for fuel planning purposes). Pilot reports of weather conditions (PIREPs) may be delivered to ATC or Flight Service for local and long-range dissemination. This information helps other pilots avoid dangerous conditions and helps weather forecasters improve their forecasting models. The 7110.65 2–6–2 PIREP Solicitation includes a note:

Routine PIREPs indicating a lack of forecasted weather conditions, for example, a lack of icing or turbulence, are also valuable to aviation weather forecasters and pilots. This is especially true when adverse conditions are expected or forecasted but do not develop or no longer exist.

Live or periodic streaming of sensor information already present on larger airliners (particularly icing status, outside air temperature, and wind velocity, but other sensors could be installed as well) would relieve pilots and controllers of having to discuss routine PIREPs on frequency and could be developed into graphical systems that automatically display hazards. Delta is using vertical accelerometers in some of their aircraft to automatically report turbulence in real time and transmit that information to airborne flights; obviously they see this as a business advantage and are loath to share it, but the system could be expanded.
Whether the costs and complexities of such a system would be worth the real-time and forecasting benefits, I don't know.