The whole conceit of DAI is that instead of burning luna at a rate of $1 they would burn it at a rate of $1.5 , The mechanism is exactly the same! And it will fail in exactly the same way.
It's far from perfect, but it is certainly more resilient and has shown to be able to pass the Lindy test.
And so did Terra. They held AVAX, BTC, LUNA and a little bit of USDC.
>150% at a minimum
And for Terra this was 100% at a minimum. It makes 0 difference.
>independent from one another
Cryptocurrency are extremely correlated.
>it managed to recover
UST itself had recovered from a previous depeg event
You keep pointing out the similarities, maybe it would help to realize that the problem was in the difference?
It did have a yield-farming component (you could mint DAI at 1% fee and put it in the DSR that would pay 2%), but that got completely knocked out in 2020. That crash was already a quite expensive lesson (tens of millions USD) for the MakerDAO team, and a lot of the investors had accepted a haircut in order to bring DAI back to the peg.
To repeat: I am not saying that DAI is bullet-proof. What I am saying though is that all the reasons you are using to make your case do not apply to DAI as it currently works.
As for "proof", you should've learned already that there is no such thing as "proof" with any of them. It's all about risk. For the fiat backed, the risk could be measured by the trustworthiness of the institution behind it and how they are managing the real fiat they have in hand. I'll risk them of my list if I hear that any of them is doing any kind of shady (we are collaterized by other assets that are not money) like Tether.
DAI and synths also have a non-zero chance of catastrophe, but at least this is mitigated by the over-collaterization. Synthetix requires something like 6x the SNX for each sUSD you can mint and their governance was not afraid to increase this requirement (and consequently reduce their sUSD supply) when their token went down.