From digging in a bit, it sounds like originally MitID was meant to be app only and it was only after pressure from a lobbying group that they relented and allowed a TOTP token.
So my guess is that this is not because they think TOTP is secure enough but rather due to the political aspects of it being centrally run by the government.
The security argument is pretty straightforward and I guess you know it already, because as you say, TOTP is vulnerable to phishing (unless you use some of the anti-bot tech I mentioned elsewhere but it's heuristic and not really robust over the long term). Whereas if you do stuff via an app, not only can malware not authorize transactions, but it can't view your financial details either - privacy being a major plank of financial security that can't be reliably offered via desktop browsers at all, but can via phones.
The alternative you propose is basically a secure hypervisor. Such schemes have been implemented in the past, but it's not ideal technically. For fast payment authorization via NFC, this is actually how it works, which is why when you touch a phone to a terminal to pay for something you don't see any details of the transaction on the display itself, just an animation. The OS doesn't get involved in the transaction at all, it's all handled by the embedded credit card smartcard which is hard-wired to the NFC radio. The OS gets notified and can send configuration messages, but that's about it.
For anything more complex the parallel world still needs to be a full OS that boots up, have display drivers, have touchscreen drivers, text rendering, a network stack, a way to update that software, etc. You end up with a second copy of Android and dual booting, which makes memory pressure intolerable and the devices more expensive. But it's hard to justify that when the base phone OS has become secure enough! It's already multi-tasking and isolating worlds from each other. There are no users outside of HN/Slashdot who would find this arrangement preferable. And as your concern is not fully technical, it's not clear why moving the hardware enforcement around a bit from kernel supervisor to hypervisor would make any difference. This isn't something that can be analyzed technically as it all seems to boil down to fear over the loss of ad blocking.
That's not actually what the article says, the article said that the rollout of MitID first included the app, and that the alternatives were made available later. The alternatives were always part of the plan. The lobby group mentioned were complaining because MitID was replacing an existing solution, NemID, which offered the alternatives. For a while during the rollout you could use both methods of identification, and the lobby group wanted to wait with retiring NemID until the alternatives for MitID were available. The old solution was not replaced due to security issues but because the vendor lost the project when the contract ran out.
There are two discussions here, the technical and the one concerned with freedom. I am concerned with both, and I think we need a compromise which doesn't throw out the latter in order to obtain a perfectly secure model.
My concern is not only with ad removal, that was just an example. My concern is digital autonomy in general, and the issue of giving an American company the power to decide what software users around the world are allowed to execute. They can censor software they don't like, and rogue governments can pressure them to censor software that THEY don't like. E.g. the EU who might want to prevent people from installing E2EE apps soon when Chat Control is rolled out.
There are good technical security arguments for phone based solutions over the alternatives, but it doesn't mean that the alternatives are worthless, just that the users have to be a bit more vigilant. I think that is a better compromise in the interest of protecting freedom and democracy.
We are some of the few people who can understand the long-term implications of the different technical solutions and the potential tools it will give private companies and governments to suppress people. If we are not advocating for freedom over convenience, then who will?
https://www.dr.dk/nyheder/seneste/mitid-kan-digitalt-udelukk...
So my guess is that this is not because they think TOTP is secure enough but rather due to the political aspects of it being centrally run by the government.
The security argument is pretty straightforward and I guess you know it already, because as you say, TOTP is vulnerable to phishing (unless you use some of the anti-bot tech I mentioned elsewhere but it's heuristic and not really robust over the long term). Whereas if you do stuff via an app, not only can malware not authorize transactions, but it can't view your financial details either - privacy being a major plank of financial security that can't be reliably offered via desktop browsers at all, but can via phones.
The alternative you propose is basically a secure hypervisor. Such schemes have been implemented in the past, but it's not ideal technically. For fast payment authorization via NFC, this is actually how it works, which is why when you touch a phone to a terminal to pay for something you don't see any details of the transaction on the display itself, just an animation. The OS doesn't get involved in the transaction at all, it's all handled by the embedded credit card smartcard which is hard-wired to the NFC radio. The OS gets notified and can send configuration messages, but that's about it.
For anything more complex the parallel world still needs to be a full OS that boots up, have display drivers, have touchscreen drivers, text rendering, a network stack, a way to update that software, etc. You end up with a second copy of Android and dual booting, which makes memory pressure intolerable and the devices more expensive. But it's hard to justify that when the base phone OS has become secure enough! It's already multi-tasking and isolating worlds from each other. There are no users outside of HN/Slashdot who would find this arrangement preferable. And as your concern is not fully technical, it's not clear why moving the hardware enforcement around a bit from kernel supervisor to hypervisor would make any difference. This isn't something that can be analyzed technically as it all seems to boil down to fear over the loss of ad blocking.