Concerns about hard disk drive longevity are justified since nothing lasts forever. One should never rely upon one and only one device for backups, but you can connect any number of external, cheap, disposable hard disk drives to a TC and add them to TM. When one fails throw it out.
For that reason, be sure to choose encryption when adding any device to TM. Otherwise that backup can be used to effectively create a duplicate of the Mac it backs up... assuming the failed hard disk drive itself can be revived long enough to work for at least a little while. Most of the time, they can.
More than one external HDD should use a powered USB hub due to the power limitations of the TC's USB port. And if you are so inclined, you can replace a TC's internal hard disk drive. Your 3 TB version is one of the more attractive options since Apple never made a TC with a capacity greater than that, but there is no limitation to its capacity or that of any external USB hard disks.
Are there other NAS devices that have a solid track record with Time Machine?
I wish there were. There is at least one experienced participant on this site who has reported good success with the Synology NAS, but in the end it's your data and no one other than you can decide upon the best backup strategy for your particular needs. Personally I don't trust anything until I verify its ability to reliably back up and restore, and the only NAS device that has been able to do that with Time Machine is the Time Capsule.
In the case of your wife's Mac I completely understand, and that's why I use TCs (or, the latest production "tall" AEBS with external hard disk drives). Nothing else is as reliable or as maintenance-free. Turn it on and forget about it.
It is my understanding that Carbon Copy Cloner can be used with non-Apple NAS devices, but I no longer use CCC myself so I can't personally verify that. When I did use CCC I found it to be an excellent program though.
Having said that you don't really need to connect an external hard disk drive other than occasionally. Once every few days is ok because every Mac that uses TM creates "local snapshots" that are completely restorable full system backups. They are flushed to the external TM backup drive whenever it becomes available. TM will begin to complain after ten days have elapsed without the opportunity to do that.
The obvious limitation of "local snapshots" is that they cannot be used to restore a Mac in the event it becomes lost, stolen, or unbootable.
... my laptop shows 17 other networks available to connect to!
That certainly qualifies as a challenging wireless environment, and whatever you see in that interface doesn't even reveal the existence of "hidden networks" that can also contribute to wireless interference. If you want to use the TC or even a non-Apple NAS, you can minimize that uncertainty by connecting it to your wireless router with an Ethernet cable. Should you decide to use the TC again you will need to start with a "hard reset" otherwise it will insist upon using its previous connection method. The "hard reset" will have no effect on any existing backups.