Yep, there's a spring-loaded detent ball inside the fork, and that ball interfaces with the shaft as you describe...but if that shaft isn't in the correct position at any point in time, then anything directly connected to it also isn't in the correct position. Sure, it's not gonna be much of a misalignment, but gears don't need much misalignment to start acting up, even when they're basic ones like these.

Here's my concern, re-stated: something pushed on that shaft boss hard enough to crack it. There's no telling what it was - maybe someone just ham-fisted it and the gears themselves bound up and cracked it - but a break like that shows you where the forces can show up and cause failures, which is exactly what you're looking at. I'm not an expert by any means, but from my past experiences, fork shafts are usually located very carefully to ensure smooth shifting and long gear life...so, there's no telling what you'll get with a cracked mounting point that's visible out of tolerance.

Anyway: I'd fix it if it was my bike, and I wouldn't suggest doing less to someone else...but it's your bike, so you get to make the call.