I've worked on a weather radar system with specs suspiciously similar to those you are describing. 250kW is a pulse power for a C-band stationary radar system, with a typical pulse length around 1us repeated 500-1000 times a second it amounts to 1/1000 duty cycle and 250W average radiated power. These pulsing parameters give about 150-300km of usable range, return signal becomes too noisy on longer ranges anyway and geometry of beam propagation means that you're shooting into outer space above meteorologically interesting part of atmosphere. It doesn't use that much power from the grid either - datasheet specs around 5kW total for all the stuff (transmitter, motorized antenna pedestal and equipment rack with a pretty beefy server to chew all that data coming from the receiver in real time). The cost aspect is pretty much in the ballpark - I've once visited our test site and the engineer pointed on the antenna horn (about paint can sized chunk of metal hanging in front of the dish full of microwave RF magic ) and told that just that piece costs about the same as a new high-segment car.
C-band weather radars existed since forever, first using magnetron transmitters and now solid-state amplifiers, though there are still a lot of new magnetron-based systems being installed, with the downside that magnetron pulses are practically impossible to modulate to perform advanced radar techniques that improve different aspects performance. There are also X-band weather radars, which operate on higher frequencies and use more modestly sized antennas (but still larger than you'd like to have on your house roof). They are more limited in range (100km-ish max) due to high attenuation and mostly used at airports, offshore oil rigs and windfarms and similar installations that mostly interested in precise local weather. They are still several hundred thousand bucks.
C-band weather radars existed since forever, first using magnetron transmitters and now solid-state amplifiers, though there are still a lot of new magnetron-based systems being installed, with the downside that magnetron pulses are practically impossible to modulate to perform advanced radar techniques that improve different aspects performance. There are also X-band weather radars, which operate on higher frequencies and use more modestly sized antennas (but still larger than you'd like to have on your house roof). They are more limited in range (100km-ish max) due to high attenuation and mostly used at airports, offshore oil rigs and windfarms and similar installations that mostly interested in precise local weather. They are still several hundred thousand bucks.