Hi, I'm the creator of Keychain.
You're right to be careful about how you use your keys.
Here are a few points for your consideration:

• 100k+ people trust our extension (20k+ on mobile Apps)
• I am a consensus witness
• There is no alternative to granting access on all websites for them to be able to make requests to Keychain, Metamask does it too.
• While the add on is not monitored by Mozilla, it is entirely opensource and can be monitored by anyone in our Hive community.
• Keys are only stored locally and encrypted

In the end, it's up to you how you decide to use your keys.
Cheers!