vi is specified by POSIX, but (at least currently) it's marked as a User Portability Utilities (UP) extension, which is optional. It is required for XSI conformance, which mandates other extensions like C-Language Development Utilities (CD). But XSI itself is mostly legacy SysV stuff; the more widely supported parts were rolled into POSIX proper and either made a requirement or grouped into their own optional extension.

In general, most utilities and functions primarily used interactively are optional in POSIX.