It's a radar system, there is not much it can do if people are transmitting on the same frequencies as it's listening on. It sends out a pulse, it listens for the response. It doesn't know that your WiFi traffic isn't a return signal from a raindrop. And it has to be quite sensitive, because raindrops are small and are not exactly purpose-built radio reflectors.
The previous approach to monitoring for wind shear conditions was to have a surface station at the airport, and hope that the conditions at the surface station were the same along the entire final approach corridor. Sometimes this was true. Sometimes it wasn't and people died. Aviation is a lot safer these days, even though we fly many more planes in the same airspace. Even an imperfect technology adds to the safety calculus.
Giving that safety and capacity up so you can use a shitty low-power low-bandwidth frequency in the 5GHz wifi band is not appealing to me. (There are plenty of full-power, 80MHz-wide frequencies that are WiFi-only. Use those!)
The FCC should have never allowed sharing to begin with. It was nice of them to try, though, given that much of the US is not in interference-range of TDWR stations.