Maybe, but what would inevitably happen is for network operators to demand that only certified devices, or maybe basebands, be allowed on their networks.
SIMs are a big reason of GSMs (and its successors') success: Having a trusted computing device to allow for key management and a few other things inside an otherwise untrusted/sandboxed phone was the compromise.
I'm all for making the interfaces used less opaque and less prone to be used for shady purposes, but the concept of SIM cards is a net win for everyone, in my opinion.
> That should be the phone's job, not the SIM card. [applications]
If you have a smartphone, it is. Many people still don't own one.
USSD is an alternative and is starting to be deployed in many markets previously using SAT, but it seems much more cumbersome to use and is less secure too (no trusted client side storage and tied to the security of the underlying transport protocols).