I’d say have backups, but then, I’d say have backups anyway. The bathtub curve is real.
More to the point: I don’t get why people can spend so much money on giant pools of storage and then get uptight when told they should get dedicated backup devices.
This is just playing media back, right? Keep a copy of the media elsewhere (and, if it's important to you, check that you can access it periodically) and buy the cheapest thing you can find for the TV.
I also do think this is massive overprovisioning, starting with the 5Gb plan, but I will suspend that. How do your computer room machines connect to your existing switch? If you have existing wall ports for them then you can get away with one 10Gb switch in the garage. If you only have one wall port in the computer room then you are correct in that they will need a switch. That switch’s single 10Gb uplink to the garage could become a bottleneck but I wouldn’t worry about that since your internet connection is only 5 anyway.
I have had a couple of drives die on me in the first year. And I have a few drives that are approaching 20 that are still working (though another one did die a year or two ago). You don’t know when a drive is going to die, only that nothing lasts forever, so that’s why to have backups.
These are all drives that were plugged in and constantly on. For drives in cold storage, I would be even more nervous about whether the drive would successfully power back on after years of being off.