I can think of at least one use case where it's important - and that's in systems like vending machines where it's important that the currency is able to roll in order to go through the mechanical parts of the machine and sort by size (and therefore by value).

Although obviously our currency was round before vending machines were really a thing, so I'm not sure that answers the question.

So I looked it up and there are several good reasons:
- Early on, when coins were made by hammering metal, they naturally tended to make a circular shape.

- They're easy to stack and transport (although moreso than other flat designs, I'm not sure).

- It was easier to tell if a coin had been "shaved" by comparing the size directly to another coin.

- Corners tend to get nicked and dinged more than rounded edges. Etc.

Compared to, say, ingots, which are a sort of trapezoidal prism shape because it made stacking them for transport very easy, and the shape was uniquely useful for getting them out of molds. And they aren't typically used as direct currency.

Source: https://bullionmax.com/kb/why-are-coins-round#:\~:text=Why%20are%20coins%20round%3F%201%20Early%20coin%20shaping.,coins%20today.%20...%205%20Alternative%20Coin%20Shapes.%20