In terms of user security, that's just not a good idea. Google has likely prevented an absurd number of account compromises (and therefore identity theft, fraud, personal information leakage, espionage...) by recognizing logins from new devices and unfamiliar locations. Google's user account security practices are pretty much the best in the business.

It's silly to think Google doesn't already know everything about every device you log in from, so that horse is already out of the barn and running on the highway privacy-wise. They might as well use that information to actually protect their users since they're already using it for advertising.