Interesting. I've been thinking about this a lot - where I currently work (I work as a night receptionist at a hotel) -- there's been a few... challenges with scheduling. I ended up setting up our current rotation that was approved by our manager -- but only for the night shift. The early/late shift still have some issues (more below).
I see a lot to like (from what I can read from the docs, I've yet to register for the demo to play around).
I do find it interesting that your example for scheduling has such a short window (I realize this is just an example): schedule to be ready to view 3 days before week start:
https://help.staffjoy.com/docs/schedule-timing
As a colleague is fond of saying: rotas and schedules aren't for knowing when you work, but for knowing when you're off (so you can plan your free time).
Does staffjoy work well with most employees on a set rotation (eg: I know when I'm off in November 2016, barring any exceptional circumstance, just as if my off-hours where every Saturday and Sunday. This is especially important when working nights -- as having consecutive days off doesn't really help much to alleviate the extra strain of working nights, if the worker cannot plan their downtime (eg: have coffee with a friend, plan to take part in a group activity etc).
I do see that you're not optimized for 24/7 work yet - which is fine of course (especially since you actually document it):
https://help.staffjoy.com/docs/running-a-247-business-on-sta...
Now, the reason I bring up rotations and long-time planning, is that I strongly believe predictability correlates with reduced stress for employees (and probably managers as well -- but your "pick-up" system for eg. sick days seems to a lot to help managers already). In Norway the law for overtime is different for managers and people that are able to determine their own hours - the idea is that if you can actually decide when you work, it's a lot less of a problem to work, say, a 100 hour week, than if someone else decides when you work.
Finally about day/night shifts -- does your system make an effort to prefer scheduling shift changes early to late, rather than late first, then early? That is the final issue I've seen a lot at my work-place -- with seemingly random changes from late to early. Apart from being illegal (late shift ends at 2300, early starts at 0700 -- meaning that there's not enough down-time to comply with local labour law, never mind local agreements with the union) -- it's an example of a completely unnecessary extra strain on the workers due to -- IMNHO -- poor management (and/or poor tools for shift scheduling).
In the general case, I think one would find that scheduling eg: 3 early shifts in a row, then 3 late shifts would be preferable to most people, rather than say 1 late, 1 early, 2 late, 1 early, 4 late -- even for those that in general prefer working the late shift.
At any rate, looks like an interesting product. I'm afraid we'll never use it at my current work place, as all purchasing decisions are centralized (for a large, international chain). But I'll make sure to mention it to friends that manage smaller businesses (that also don't operate 24/7 - so a better fit overall :-).