"Streaming" implies a constant flow of data in a way that the available bandwidth of most present aircraft data/communication systems doesn't support. It isn't inconceivable to route those sorts of sensors to an aircraft internet connection, but the present state of things is much more based on ACARS -- which is essentially a text message. Sending a message every 10 minutes with winds aloft and temperature is entirely adequate resolution for the weather prediction systems, anyway.
It would certainly be possible to theorize a real-time wind readout from each aircraft to the controller so that he'd know the effect that wind would have when he gives a vector or a speed adjustment to an aircraft, but the value to be gained isn't all that great. If every aircraft on a given arrival flow has been assigned the same heading & indicated airspeed, they'll all end up doing the same thing, even if the controller is having to guesstimate the winds based on the delta to their ground track from his assigned heading. (Speeds never match anyway: assignments are given in indicated airspeed, but observed in groundspeed, which is true airspeed +/- the tail/headwind component.)
There is a case where it would be nice to have the wind values from a preceding aircraft, and that is in descent planning -- knowing the actual winds from cruise altitude down to 10,000' would allow a sufficiently smart FMC to build a more efficient idle descent path. Nice to have, but probably not such an improvement over the current state of forecast winds as to make a big technology investment worthwhile.
Likewise, knowing what the winds are at various altitudes could better inform the decision when & if to climb to a higher cruise altitude. Today, it's a matter of having a preflight weather forecast, and asking ATC if they have any aircraft at the other altitude that can provide a PIREP of winds and ride. Again, nice-to-have, but only that.