Why do some researchers use the oxymoron "prevalence rate"?

An incidence rate (whether an incidence density or an incidence proportion) measures the probability of an event (typically a new case of the relevant health condition in epidemiology) divided by time. Incidence rate: probability of new cases over time.^*

A prevalence (whether a period prevalence or a point prevalence^**) is not a rate, as there is no probability of new cases over time, but just the probability of individuals being a case at some point in time (except the instantaneous measurement implied by "point" doesn’t truly happen all that often, and so prevalences are situated with respect so some period of time like a day, or year). Prevalence: probability of being a case during some period.

Lots of respectable epidemiology textbooks make this distinction (i.e. between rates and prevalences, and being explicit that the latter are not rates), and yet, some epidemiologists are quite happy to publish "prevalence rates". For example, the CDC says:

Prevalence, sometimes referred to as prevalence rate, is the proportion of persons in a population who have a particular disease or attribute at a specified point in time or over a specified period of time.

Wherefore "prevalence rate"? (Really, it just makes me twitch when I encounter the term, but I wonder if there is a good story or history there, or a nuance I am missing?)

^* A rate is a more general concept than incidence rate, specifically. Rates imply how much of one thing happen given another thing; for example, the rate we term speed measures how much distance happens over time.

^** I suspect all prevalences are technically period prevalences, as instantaneously concurrent measurement of, for example, health conditions, makes less sense at shorter and shorter period intervals.