[0] https://en.wikipedia.org/wiki/Equivalent_isotropically_radia...
Basically APs on 2.4 GHz are only allowed 36 dBm (4 W) EIRP, no matter what antenna shape. This is usually not a problem though, since stations tend to have weaker transmitters anyway, but will still benefit from the AP's enhanced antenna gain.
If I aim my antenna such that I contain the illegal power region within my property, will there be an unintended consequence?
To be clear, I'm referring to a house not an apartment so I don't have any concerns about upstairs or downstairs neighbours.
The domain of the FCC extends to all property of the United States of America, be it public or private.
You could place sufficiently absorptive materials that this isn't so (e.g. enclose your house in a Faraday cage). But as hydrogen18 points out you're still limited by the FCC.
His rules: 1500 watts PEP, unlimited EIRP, channels 1 to 6 only, no encryption
That's better than a normal microwave oven.
http://w5vwp.com/wifihams.shtml
(Of course then you are subject to all the Part 97 restrictions like no encryption, no commercial use, etc)
1: http://hraunfoss.fcc.gov/edocs_public/attachmatch/DA-00-2225...
That being said if you're using this in your home/office on a legal channel it would be really difficult to even tell from outside you were using it and almost certainly not worth the FCCs time to even try to watch for it. It's not that much extra gain over the stock antenna.
The antenna is not supposed to be replaceable, hence the reverse SMA connector on most modems.
Modifying the antenna in any way invalidates the type approval.
Because it's illegal, is why.
No doubt this accounts for some of the "my WiFi doesn't work upstairs" stories.
You can buy directional APs if you want, but they're usually used for outdoor point-to-point links, or as sector antennas. e.g. I just installed one of these today: https://routerboard.com/RBSXTG-2HnD in a place that needed a signal far from where the AP was. Usually patch antennas (like this product) are preferred over Yagis for microwave links due to their smaller footprint, and capability of dual polarization in a single package.
Better is if your indoor AP can transceive in more of a "pancake" shape, like this: https://routerboard.com/RBOmniTikU-5HnD Note that's almost the same gain as this home-grown Yagi (7.5 dBi vs. 8.5 dBi) but with a more useful directionality.
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.