Full keyboard support matters for several overlapping groups of users: people with motor disabilities who cannot use a mouse precisely or at all, blind screen reader users who navigate primarily by keyboard, and power users who simply prefer it. WCAG success criterion 2.1.1 requires that all functionality be operable through a keyboard interface, and 2.1.2 requires that focus never gets permanently stuck (a keyboard trap).
The fastest way to audit keyboard navigation is also the simplest: physically unplug or disable the mouse and try to complete a core task, like adding an item to a cart, using only the keyboard.