>You're getting caught up on redundancy for a given total number of disks, and in the process missing the point entirely.

That is the only point. Let me state it like this: you have N disks of which you want to get M capacity out of (M < N), what's the RAID configuration that maximizes redundancy. My assertion is that parity raid is strictly better than RAID10 at doing that, you haven't really refuted it.

>From there, my point should be more clear. Just like how you can constantly add more and more parity blocks (and disks to handle them), I can constantly widen the mirror.

Of course you can, and for any given number of disks you'll always be behind on redundancy. You can of course just throw more hardware at the problem and if your choices are between RAID6 (2-parity) and RAID10 then RAID10 eventually wins because you need more parity disks than RAID6 provides to take advantage of the extra hardware. Since most block RAID implementations only do 2 or at most 3-parity, RAID10 ends up being the only practical solution for lots of disks. But for a 4 or 5 disk setup (most NAS applications for example) RAID6 or ZFS 3-parity support is a better choice if the performance tradeoff is workable (as it is in most NAS).

>because with a n-disk array, a RAID1 will always be at least as redundant as the equivalent parity-based RAID

This is a red herring, yes there is the lower bound of no implementation with N disks can survive the loss of all N disks, and if you want the space of only a single disk RAID1 of N disks is the obvious choice.

(really, it'll always be able to survive one more disk failure than an n-1 parity-block array; you can see this rather easily when comparing RAID5 with a three-way RAID1).

This is again wrong. A 3 disk RAID1 has the size of 1 disk and a 3 disk RAID5 has the size of 2 disks so they're not the same. To make it comparable you need to make the array RAID6 at which point you have the same space and redundancy. You'd still do a RAID1 though as for the 1 disk size case there is no added benefit of parity.

>RAID10's advantages become more clear, since each mirror group added to the striped whole instantly bumps up capacity and the best-case without compromising the worst-case. Meanwhile, you do have the advantage of having more flexibility in the quantity of disks added, but doing so doesn't help your best-case unless you feel like resuming the whole "let's make every disk a parity or mirror disk" arms race.

This is missing the point entirely. The parity normal case is the same as the RAID10 best case and better than the worst case. There's no real way around that.

>Which is exactly why you're incorrect. Since any disk failure is like any other, every single disk has to be unique in order for a parity-based array to benefit from any diversity

This is just not true. Having diversity means that failures become uncorrelated. Parity RAID explores that even better than RAID10. The property you keep bringing up is basically saying "since RAID10 has worse redundancy than n-parity it benefits more from uncorrelated disk failures" which is true but only by partially mitigating a problem that parity RAID doesn't have.

>This has been a fun discussion, and there is certainly lots of room for debate on the merits of mirroring v. parity, but I'm starting to think that we should just agree to disagree on this one.

I think that by now I've explained my point clearly enough and even repeated myself a bit so yeah, I'll drop it here.