Because if it can be proven in court that the ID was identifiably fake, they can be held liable for any damages should the minor become intoxicated. “Checking” an ID means there was a reasonable attempt to verify the legitimacy of the document and that it matches the individual using it.

Since what is identifiably fake is a somewhat vague category that can be litigated in court, most bar and booze store owners try to err on the side of too careful–which usually just leads to annoying people–rather than not careful enough, which can lead to fines, damages, or the loss of license to serve alcohol. Any of those can be bad enough to close a business.