Hi danymarc,
Last night, I searched for articles about all that you wrote after reading your post. You are correct, it doesn't mean to be used that way.
You have so much knowledge and expertise, thanks ;)
Sectoral antenna costs about US$100 here, but not TP-Link.

Digging and digging, finally you have the hole!
Here is how it works. Just need to use same url as referer then will work again
Using cURL:
curl -L --user admin:admin http://192.168.1.1/userRpm/SysRebootRpm.htm?Reboot=Reboot --referer "http://192.168.1.1/userRpm/SysRebootRpm.htm/"