The Navy offers a similar online time service although it is clearly far less developed from a design perspective (https://www.usno.navy.mil/USNO/time/display-clocks/simpletim...). However, what's perhaps more useful is that the Navy continues to offer a telephone time service (202-762-1401) while NIST does not. Additionally, the GPS time, while operated by the Air Force, is precisely synchronized to the Navy time plus or minus a known offset (due to the decision to no longer apply leap seconds to the GPS constellation to avoid leap-second-related problems).
There is some history here. The NIST is interested in timekeeping from a metrological perspective since it is important to many commercial and scientific pursuits. The Navy, on the other hand, has long been interested in accurate timekeeping because it is required for celestial navigation. The transit telescope maintained at the Naval Observatory comes from the legacy of the Naval Observatory as a tool to correctly adjust the clocks used by ships at sea for navigation. Similarly, many of the most significant advances in mechanical timekeeping were spurred by the need for compact and reliable clocks for use at sea.
The Navy operates master clock equipment at Schriever AFB for closer proximity to the NIST equipment at Boulder, but the primary means of comparison of the two time bases is by observing the GPS time. Because of the simplicity and low cost of GPS time sources, GPS is as ubiquitous for time measurement as it is for navigation.