USB 3.0 ports on Late 2013 iMac

This is not my area of expertise, but I have to say: just trying to follow all the ports and things you have plugged into, I would question if the USB ports actually have enough power to power all of that.Are any of the hubs self powered or do they all draw the power from the Mac?

I would stop by a Genius Bar and have a chat with them; I would also check with them and System report to see what the actual power limitations of the USB ports are and what the power requirements of your hubs/devices are.

Glad to hear they draw their own power; however, I still think it is overloading the USB ports - after all, the iMac is a consumer product. Hopefully someone with knowledge in such matters will chime in; I'll be sending out a bat signal.

could be a bad hub or bad port. Have you tried pluggin one of the other hubs into that port? Does it work?

What if you plug in the bad hub by itself, does it work then?

I'd wonder whether somebody here will get to the bottom of this, short of guessing at triggers and swapping parts, and the Apple support folks you've directly discussed this with have undoubtedly already provided that and some related suggestions. Whatever's going on here is likely configuration-specific; bad cables, flaky or bad hubs, or problems with a device. Even the flash devices can be flaky; there are various ways those can be wrong or different, or the file system formatting can sometimes itself be wacky.

The usual and best way to troubleshoot these cases involves a USB bus analyzer, and those aren't the cheapest devices around. Via a bus analyzer, one apparently-working configuration showed ~30% of the entire USB bus bandwidth was going to error and error-recovery traffic, and that's not the only weird stuff I've seen transpire on USB.

Failing that analyzer availability, you might try scanning your USB bus with the USB Prober tool, which is an add-on component for Apple Xcode; part of the hardware I/O tools. (I think the USB Prober tool is only available with membership in the Apple Developer Program; AFAIK that tool not in the App Store freebie Xcode download.) That'll show you some more details of what's actually visible to the OS X host system. Also see the associated Apple QA1370 USB technical QA. That might show some additional details that might point to a trigger.

Alternatively, simplify the configuration, and consider moving the printers and scanners out onto the local network — host-attached printing devices and related have never been a particular favorite of mine — and consolidate the disk storage into fewer enclosures and possibly also migrating from USB 3 over to Thunderbolt or out onto network attached storage (NAS) devices as appropriate. The Apple support folks you've chatted with have probably also suggested something similar.

Crashes can be due to host software bugs, or software bugs secondary to USB level hardware weirdnesses. The Apple folks are the only ones in a position to dig through those crashes and figure out what happened. On the few occasions I've hit similar bugs (most recently with a KVM), the Apple engineers did follow up with some interest.