Hi Jonathan,
Funny...I was just coming back to this to add an edit to my post, regarding my use of the term backfeed breaker. I was going to add that my use, here, might have been unclear. In normal use, a backfeed breaker is one that's installed in a panel and which feeds energy into the panel (as opposed to drawing energy from the panel) as in the case with lots of grid-interactive (grid connected) inverters and devices. Per the standards, a breaker is suitable for backfeeding (also called reverse-feed) unless it's marked with specific line and load side markings, in which case it's not rated for backfeeding.
"Per UL 489 Paragraph 9.1.1.13: Circuit breakers shall be marked
“Line” and “Load” unless the construction and test results are
acceptable with the line and load connections reversed."
It's common to use such a connection in grid-tied systems. It's also covered in NEC 705.12 (which discusses this and a related 120% busbar feed limit). This panel isn't grid interactive, but I used the backfeed term to distinguish the direction of electrical flow through breaker and into the bus bars.
I do agree that this configuration has the theoretical potential to draw 120A through that source/line cable...but I'd presume the source (inverter) has a limit on the output. However, yes to be safest, that single cable should be sized to safely carry the max possible current flow...which would be limited by the source (an inverter limit or some OCPD near the inverter) OR by using a smaller breaker in the panel. And yes, as you suggest, a single breaker could be installed on the source/line cable and then the output of that breaker could be split to feed each leg of the panel...but this panel doesn't have lugs on the legs/bus bars, so they'd have to install a separate box with a breaker that would then feed into this double-pole breaker anyway (since that's how this panel is designed to be energized).
I do admit that I presumed...which isn't good...that the line to this panel is protected or limited earlier in the chain. Any OCPD in the panel, like this breaker, won't offer any protection to chafing or rodent chewing or other compromises or shorts before the panel.
Anyway...all good things to think about and the key takeaway is that all wires should be protected (as close to the source as possible) with appropriate over-current protection.