I used to think that but then I realized that you would also have some parts of the world where the date switches over in the middle of the day. I mean it is certainly odd that different parts of the world are on a different day than other parts, but I think switching the date in the middle of the day is a bigger issue.
Is it a bigger issue than signing and dating a document while in a different time zone from the one the document needs to be dated in? E.g. signing a contract on the west coast when the contract needs to be dated on eastern time because of regulation X by agency Y. What if there are multiple regulatory agencies that want you to date the document in different time zones? e.g. the SEC and the ECB.
I would argue it makes the most sense to date all legal documents in UTC and using any other timezone would be a confusing mistake. But we can disagree.