It sure did have such setup.
SIM cards can have micro applications that get exposed via the "SIM Services" menu entry or something similar named.
That is how before the WAP days, the carriers used to offer SMS based applications.
Re:Decap of a Cell Phone SIM card [video]
by Nullabillity on Monday October 10, 2016 @09:56AM
(#12677087)
You want compute in your SIM card, because you don't want to expose the actual secrets to the phone.
Same thing with (modern) credit cards: you can send a transaction and a PIN code, and get a signed transaction in return, but you can't fetch the keys and sign arbitrary transactions afterwards.
I am quite sure that my first SIM card, 20 years ago, didn't have such setup and worked, quite the same.