If that's the case, then none of a tanks gear matters either.
The argument you are making is essentially small increases to survivability don't matter, and don't add up to something significant. There's a recent people min-max, especially tanks. There's a reason we try to squeak out every tiny bit of avoidance, or armor, or block, or health. Because it matters.
Trying to say it doesn't matter is ridiculous. That's like saying the armor difference between DK's and Paladins/Warriors doesn't matter, when clearly it does.
It's actually a very sound argument.
It boils down to healer mana, healer throughput, and EH. When you start out raiding and healers can oom, any healing is worthwhile. It is very valuable. However, healers get gear and stop ooming while tank healing. That has happened through the last few expansions. They just don't oom while healing tanks unless they burn really expensive heals; with a bit of gear, even that doesn't hold true. EH takes over and when that happens, small residual heals do very little.
The reason DK and pally / warrior armor matters is because of EH. You do realize that a DK only takes about 4 to 5% additional damage (post-armor and mitigation) compared to the others, right? Our heal is for 29% of the previous damage. Even with 50% overheal while using DS horrendously every 10 seconds, the DK is getting more healing than is necessary. Why aren't DK's OP because of it? The reason it isn't OP is because the healers stop ooming while tank healing. EH takes over. That is the reason DKs can struggle in heroic raids. It only becomes useful when the content is trivial enough that the healer can sit there being bored or the healers are all focused on raid healing (That's right; that is exactly where DKs become OP). EH really is at the heart of the issue.
Small boosts to EH are important. Small cuts to healing, when your healer can't oom and has nothing to do, do very little in this game. There has only been one difficult encounter where tank self-healing was truly powerful. That was H-General in Ulduar. Healers could oom and that self-healing counted for a lot. (Not that paladins could really do it; they were bad on that fight). However, a DK really trivialized it. They aren't wrong, small heals do very little in the long term. Popping a large heal after burst is helpful. Small heals do very little unless all your healers are bombing the raid. Healers don't oom and that negates the power of self-healing. The reason avoidance and mastery are still important is because when the tank can last 3 hits or so, there is a really high probability of avoidance or block. The probability of hitting your EH is extremely low, which is helpful to your healers.