What was the use-case for the 74hc590?
The use case is pretty well described by you: a binary counter with a latch. 

For when you want something counted, but the output of the counter to only change on a latch signal.

Use cases range pretty widely – from gated clock dividers to clock-domain crossing counters to very simple IO expanders.

A very striking example is a frequency counter: assume you want to measure something in the range of 20 kHz. You have a 100 Hz clock. You use that 10 Hz clock to reset the counter clocked by the ca 20 kHz, so counts should be always in the range of around 200. Of course, you don't want your display to update while your counter is counting – only maybe 12.5 times a second. So, you latch your counter on the 8. edge of your 100 Hz clock.

(these ICs weren't all invented to build CPUs, so the assumption that "it exists" and "it must be useful in a CPU design" is unfounded)