By that logic, there’s also no such thing as a meter either. It’s defined as a distance light travels in a time interval proportional to the inverse of a frequency related to the caesium-133 atom. Definitions don’t mean there’s “no such thing” as something, it’s just a matter of if the units are useful in a given context. And meters are more useful in most everyday contexts.
In timekeeping, there are so called stratums to describe how correct a clock is.
Stratum 0 is a physical process, an inherent property of the universe. An atomic clock would be stratum 0.
Stratum 1 is a clock defined based on a stratum 0 clock. For example, GPS clocks are usually stratum 1, so are timeservers at universities with atomic clocks.
Stratum 2 is a clock defined based on a stratum 1 clock, for example, your router’s ntp server if it syncs its time based on gps or a university’s timeserver.
So if we adopt this jargon for units:
Meter is a stratum 1 unit, defined based on the stratum 0 properties of lightspeed and cesium resonance.
Inch is a stratum 2 unit, defined based on the stratum 1 meter.
