I'm about to buy two ESP8266 modules. I want them to use as an auto deauth device. The first module will monitor my WiFi router's packet transmission. If a certain device receive loads of packets from my router (which hogs my network) the second module will deauth that device or flood "forged" packets. There will be a threshold so a simple web browsing will not trigger the deauth process from the second module. Btw. My router doesn't support traffic shaping & QoS. Only a different kind of QoS (DHCP & IPP/TOS) which is useless because my ISP doesn't support it.
You're going to face significant challenges with this.
The ESP Arduino API doesn't let you run in promiscuous mode (which you'd need in order to see other people's traffic), and the APIs are all set up for you to create nice well-behaved traffic, not spoofed packets.
I strongly suspect the hardware can do it, but you're going to be making significant changes to the IP stack. The code is all open, so you're free to dig in and see what you can do (I've done a similar thing myself, as I needed some lower-level information than was made available in the API).
So feasibility is determine by your skill level (C, C++ and IP stack and protocols) and available time.
Something like a Raspberry Pi Zero and a suitable USB wifi dongle would probably be a quicker path at similar cost, as there are Linux tools to do a lot of this stuff.