Many, perhaps most, references to decimal time of day refer to it as "metric time". I have noticed, however, that advocates of the metric system get annoyed by those who want "metric time" added to the metric system, because time is already included! Although the original metric system did not include a unit of time interval, the modern SI metric system does: the second. Standard metric prefixes are commonly applied in scientific use, including milliseconds, microseconds, nanoseconds, etc. However, larger metric units are not as common, and SI has compromised by allowing non-decimal multiples, such as minutes, hours and days, to be used with metric units. So the problem with metric time is not that there is none, but that metric and older units are being used together.
Any arbitrary unit of time would work as a metric base unit. The second has been adopted, but it could have been the day or hour or anything else. The real issue is how to divide the day so that people can organize their activities. The metric system does not help, since there are 86.4 kiloseconds in a day. So instead we still use hours and minutes.