What information from your login keychain do you expect to need on your new computer?

There's not really a plausible answer to that question, because the login keychain data is almost entirely specific to that host.

To iron-man your argument: Apps that store account credentials to third party services will need to be signed in again.

If you were using http basic auth for a website and saving that, then it was probably in there.

Private keys and certificates you manually imported, or that were created by an application for your host. This is the closest to a plausible answer, imo.

Then you're in trouble.