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Honestly I think you covered why Tatami safejump is often preferred. I can elaborate though, for why at least I think the things you highlighted are a big deal.
Covering backdash is really really nice, given there's a macro for it.
IBFD is also a really important thing to be able to avoid. If you opponent IBFD's a jH then you don't get a cS after, which will greatly affect your ability to run mix. Your opponent can back dash to avoid a youzansen / 2D, and jump to avoid a 2H, effectively gutting your mix, turning it into a guessing game for you too, instead of a nearly strictly good situation for you.
By being able to run mix after Tatami OR the cS following tatami, you also make it difficult to YRC your mix once you incorporate BRC into your high / low game. This is lost if the represent backdash or IBFD after jH. If they're able to IBFD you out, or backdash and potentially only eat a fS, then you effectively have given up your strongest situation.
Something else to mention, IBFD / back dash are MUCH less committal than a DP. If they can accomplish "get out of mix" with those option as opposed to having to fire off a DP that's a huge deal. If you block the DP they lose the game pretty much immediately, but if they can represent those other two options instead, the situation is honestly not that bad considering they lost neutral a moment ago.
On the note of OSing the situation, while you can't really beat both H-DP on wake up and post tatami, the former is generally more common, and it's not too hard to beat H-DP on wakeup and mash post tatami. If they are just ripping DP post tatami you can gamble around that if you want, either by going straight into cS / mix on their wakeup (losing to wakeup H-DP) or waiting it all out to see what they do. Because tatami forces DP as opposed to less risky options to interact, it's a losing situation for them generally.
That's just my perspective on all of this, take it with a grain of salt obviously
Also I should mention, I think it's good to do both
