What is the legality of this? I have a vague suspicion that operating a device like this would violate some FCC regulations.
Right? Why wouldn't the router companies include this somehow in their designs if it actually improved performance? Because it's illegal, is why.
It's not all that useful indoors though as 2.4 and 5GHz signals bounce off of walls really well so you lose much the directionality at the very first wall it hits.
1: Actually there is a total ERP requirement, but most routers with external antennas are already close to that requirement, so more than about 3dB gain will often put you over.