The little $h$ is a historical artifact, one that will probably die out soon enough.

The thing is, $H_0$ was extremely difficult to measure precisely for many decades after its importance was realized. At some point, cosmologists were divided between the "$H_0 = 50\ \mathrm{km/s/Mpc}$" and the "$H_0 = 100\ \mathrm{km/s/Mpc}$" camps. Because the quantity appears as an overall scale factor to some power in many cosmological formulas, people adopted $h$ to be $H_0/(100\ \mathrm{km/s/Mpc})$ by definition. Rather than plugging in their preferred value of $H_0$, they quoted formulas in terms of $h$ and its powers, so that others using different values of $H_0$ could compare to them. All $h$ does is make undoing someone's erroneous value for $H_0$ easier.

Today, we know $H_0$ to a few percent or so, and few people lose sleep over the imprecision. Since there is nothing physically meaningful about the $100\ \mathrm{km/s/Mpc}$ scaling, it is $H_0$, not $h$, that is more fundamental.

The little $h$ is a historical artifact, one that will probably die out soon enough.

The thing is, $H_0$ was extremely difficult to measure precisely for many decades after its importance was realized. At some point, cosmologists were divided between the "$H_0 = 50\ \mathrm{km/s/Mpc}$" and the "$H_0 = 100\ \mathrm{km/s/Mpc}$" camps. Because the quantity appears as an overall scale factor to some power in many cosmological formulas, people adopted $h$ to be $H_0/(100\ \mathrm{km/s/Mpc})$ by definition. Rather than plugging in their preferred value of $H_0$, they quoted formulas in terms of $h$ and its powers, so that others using different values of $H_0$ could compare to them. All $h$ does is make undoing someone's erroneous value for $H_0$ easier (sort of).

Today, we know $H_0$ to a few percent or so, and few people lose sleep over the imprecision. Since there is nothing physically meaningful about the $100\ \mathrm{km/s/Mpc}$ scaling, it is $H_0$, not $h$, that is more fundamental.