Be careful not to equate the SIM card with a password (something you know) rather than a token or smartcard (something you have). When you are dealing with a password, you are creating the secret. In the case of the phone connection, you are actually giving the provider back their secret, you do not set it. If you buy a pre-paid sim, often you can just slip it in and you don't need to setup an account; if you were to sign-up through some app or on phone mechanism you would likely need an account and other overhead in many cases.
That said, there is no practical reason to require a sim card. CDMA phones do not require a SIM card, but (per Unlocking 101: Difference Between CDMA and GSM)
GSM phones can be unlocked using a passcode that the manufacturer has
(or that can be generated using a keygen similar to a keygen for a
hacked cd rom for your computer). Once that passcode is entered the
phone will allow the use of any SIM card in the SIM card slot.
on the other hand, doesn’t have this unlocking passcode feature since
it doesn’t have the GSM standard locking mechanism. Instead, CDMA
phones must literally be physically flashed with different firmware
that has the new CDMA carrier’s information in it for the phone to
access that new network (in other words, to unlock a CDMA phone you
need to literally plug it in and use a flashing software to flash the
carrier you want to use’s information onto the phone).
You could certainly have a setup similar to wi-fi connections with a captive portal. But the way a cell provider network and a wifi network operate, the segregation of traffic, quality guarantees, etc. are different.
There are also practical reasons to have a sim card. The sim card can store information, contacts, etc. More practically, remember there was a point in time where cell phones didn't have apps, internet connectivity, etc. Even today, to require an app based solution would require a lot of work and brings in potential software issues. The SIM solution seems to be less prone to user error or user frustration. It also simplifies support processes. Probably most important is that this is the way it was, and to implement the changes would be costly for providers to replace all of the infrastructure, train call center and sales reps, etc with minimal overall advantage to most customers, who often don't care. You see the same argument come up frequently for cable TV vs CableCard and set-top-box.
While you state this as a problem:
much more accessible because users don't need to organize to have a
physical thing sent to them for every device
there may be others who really like the idea of just slipping out a card and moving it between phones, for some this may make more sense.