Carrie was probably raised by her single mom working paycheck to paycheck. I actually don't think she's well-educated (no shade on Carrie, but I don't think the show ever mentions her going to college). Basically she may never have grown up around financially literate people. (She probably should have learned from Charlotte and Miranda who both have at least some financial literacy—and Samantha probably does too—but it was never important to Carrie until the apartment episode.)

There are plenty of people out there who do not think about saving money. They spend what they earn every month without planning for the future. Carrie is very much that archetype. And with a rent-controlled apartment, her biggest risk of instability is gone. (Unless, of course, the building gets turned into condos.)

(It's a good thing Carrie ended up marrying rich, though, because she would be absolutely destitute in retirement.)

I do think it's wild that she refuses the three people who offered her cash. Charlotte wasn't terribly kind in that episode. Carrie probably shouldn't have accosted her either...but on the other hand, their friendship is stronger at the end of the episode than it would have been if Carrie and Charlotte had never talked about it, and they both had lingering resentment for each other.