I think that this is only a matter of convenience. We really need a standard way to express mortality rates so that they can be compared against thresholds, between populations, and between time periods for the same population.
A number of standard formats are used:
deaths / 1,000 population / year : This is most often used to express mortality in stable populations. We often see "1,000 populations" replaced by "per 1,000 live births" in U5MR estimates.
deaths / 10,000 population / day : This is what we are used to in humanitarian populations when we expect mortality to be high and changing rapidly.
deaths / 1,000 / month : Not in common use but may be seen in stable camp settings (i.e. after the immediate crisis has passed).
Other demoninators are used. For COVID we often see 100,000 in the denominator:
Population New York City as of 1st May = 8,398,748
Estimate count of COVID deaths as of 1st May = 23,430
That is 23430 / 8398748 * 100 = 0.2789702% dead from COVID. This might be expressed as:
0.002789702 * 100000 = 279 / 100,000
I have seen this expressed as deaths / million population.
Using these standard formats makes it easy to compare rates. If we did not have these standard formats we'd have to work raw counts. For example. what is the proper interpretation of thes two rates?
(1) 271 deaths in 158,934 persons over 13 days
(2) 445 deaths in 72,072 persons over 47 days
We have all the data we need but the true relation is that the two rates are similar to each other is not obvious at first glance:
(1) 271 / 158934 * 10000 / 13 = 1.31 / 10000 / day
(2) 445 / 72072 * 10000 / 47 = 1.31 / 10000 / day
The standard formats also makes it quite easy to convert between formats. So that (e.g.):
1.31 / 10,000 / day
is the same mortality rate (risk of death) as:
(1.31 * 365) / (10000 / 1000) = 47.8 / 1,000 / year
Moving between with 100,000; 10,000, and 1,000 is simple. Moving between follow-up periods is less straightforward arithmetic. No problem with a calculator / software and taking care to keep track of time.
I hope this is of some help.