Why would Preview "want to use" my (unused) login Keychain just to execute hotkeys?
Short answer: It doesn't.

Long answer: There are plenty of reasons why this may occur. I discuss a couple of scenarios below.

If you recently changed your password, I would recommend reading this support article from Apple. 


  The password of your macOS user account might not match the password
  of your login keychain. Either create a new login keychain or update
  it with your new password.


If this is not the scenario for you, or if that article does not solve your problem, there are other probable scenarios. Sometimes, after updates, the Keychain may become corrupted. Using Keychain Repair from the Keychain App, you can easily fix this problem. I would refer to this answer for more information.

I have been personally facing this issue since El Capitan, and only recently fixed this issue. When El Capitan was released, this bug was introduced to some users using FileVault. Disabling FileVault and re-enabling solves this problem as well.

For additional solutions, I would refer to other answers left in similar questions:


How to stop my machine asking for multiple passwords when I log in? by klanomath
OS X is repeatedly asking for login keychain password by Andrei Glotov