With the LOTH it’s not a question of the faithful knowing or not knowing whether one particular priest or another has prayed his obligation. It’s a question of praying for the entire Church, and that prayer be continuous. The LOTH assures that prayer vigil over the entire Church. It is a serious obligation, and for instance for Benedictine Monastics the LOTH is known as the “work of God”; the motto “Ora et Labora” (pray and work) has many layers of meaning, one of which is that the Divine Office is both the Ora and the most important Labora of monastics.
It is of the utmost importance to everyone in the Church, to maintain solidarity with all regardless of one is in a state of joy, suffering, nearing death, fallen away, etc. Especially for those in difficulty.
The faithful may not know if a priest skips his obligation or not, but the faithful should know that priests, religious, and an increasing number of the laity, are joined in continuous prayer for all of us. Without the obligation, that continuous vigil would surely start to fracture, given the foibles of human nature.