Many people today don't even own a computer and do everything on their phones. Teaching the masses safe habits rather than convenient ones is a difficult problem, most don't care.
The point is offering something already usable and gives people a habit on that. After we might add yubi for generic services like GMail and so on.
In 2024 having a card reader is indeed not that great, but I still have the one given by my bank ~20 years ago, as it's a strong factor which I can use to set up weaker second factors (typically push notification to the mobile app, nowadays).
We could imagine several ways people link their real, physical government ID to a trusted device. Every smart phone has had a built-in security key for the past 5 years or so. Banks have to check your ID at some point due to KYC. We could kill multiple birds with one stone.
Similarly various countries offers eIDs (some I know Estonia, Belgium, Italy, Germany, France) witch are NFC ISO 14443A/B who are used to authenticate the Citizen on various public services.
Many universities and some high school as well offer an NFC badge witch is a smart card, and could be used to authenticate institution website and so on.
All those examples are already in use since years, but used for limited activities and mostly not advertised. It's just a matter of spread them. In Italy for instance since some years national eID card (CIE) is used to access fiscal services to send for instance you filled tax forms, to pay some tax and so on, while national health service card is used to buy tobacco from every automatic vending machines since much more (to prove you are >18 years old), France start since last year the same with France Connect+ witch as Italy, German etc is the pan European eIDAS system to offer digital docs and services to all. All countries have invented absurd systems to AVOID using eIDAS with smart cards in most cases, while we all have them. Only to push the "app" cloud+mobile model.
I keep my Yubikeys in a drawer at home and use my phone as day-to-day security key.
I use a wallet that holds cards, but not common or popular, and are you seriously suggesting that we insert this thing into our phones, which would probably mean you'd have to dislodge from the case, wallet or not, and align the card into the slot. Not to mention how much space it'd consume in a smart phone. You & maybe a very tiny cohort want this, the general public don't, especially for the marginal security benefit. Anyways as others say, the modern equivalent is NFC, but again getting everyone to buy and carry an accessory is asking too much. Modern smartphones already have modern security and in recent years have been exposing their security coprocessor chip to the OS.
I use it normally to declare my taxes for instance, with a small desktop card reader (ReinerSCT CyberJack) as a "security device" in Firefox to authenticate for instance, just putting the card on the reader, open firefox going to the relevant website, click on eIDAS login, entering the national ID card PIN and being in. A pin for all public sector services, no apps needed, no regular password changes and so on.