[Question] What explanatory power does Kahneman’s System 2 possess?

In the 70s and 80s, Kah­ne­man and Tver­sky did a bunch of pi­o­neer­ing re­search on heuris­tics and bi­ases in hu­man thought. Then, in Think­ing Fast and Slow, Kah­ne­man di­vided hu­man cog­ni­tion into Sys­tem 1 and Sys­tem 2 - ba­si­cally, Sys­tem 1 ap­plies quick heuris­tics which are prone to bi­ases, and Sys­tem 2 does the slow, effort­ful think­ing.

But what does Sys­tem 2 ac­tu­ally add to the the­ory in terms of ex­plana­tory power? Con­sider an al­ter­na­tive ver­sion of Think­ing Fast and Slow in which Kah­ne­man wrote some­thing like “Here are the con­di­tions in which hu­mans use this mode of rea­son­ing I’m call­ing Sys­tem 1, which is fast and ap­prox­i­mate and effortless and uses heuris­tics and demon­strates bi­ases which can be de­tected in cer­tain ways. The rest of the time, I have no idea what’s go­ing on, ex­cept that it doesn’t dis­play the traits that would qual­ify it as Sys­tem 1 in­fer­ence.” In what ways would this be less in­for­ma­tive than his ac­tual claims?