This is an excellent point. However, the carefree attitude may not necessarily be a personality trait but due to lack of confidence.

It is wise to have, at the very least, the knowledge to repair a flat. This is typically the issue one would encounter most (yes, I know, someone will chime in and say that they've busted spokes or cables more often than flatted).

At the risk of sounding sexist, I mention this as an interesting fact:

In the bicycle safety courses I give, we cover the basics of bicycle maintenance; flat repair, gear adjustment and brake adjustment, in addition how to safety-check your bike, know the parts and identify a problem.

Women are more incllined, than men, to take a safety course (because men obviously know everything)

But when it comes to maintenance in those safety courses, I more often than not hear from the women;
"I have a husband for that"
"I have a cell phone"
One lady even said, "I'll just sit on the side of the road and cry until some guy stops to fix it for me."

This seems to be a combination of a lack of interest in maintenance and a lack of confidence.
I often have to step in and shut the males up (because the issue often goes off on a tangent) to allow those ladies to learn the particulars.

Admittedly, when I first started teaching, I had to learn to see the issue from their perspective. In general terms, females often lack the hand strength to get a tire back on over the rim, for example, so we have to discuss ways to do this.

So, maybe carefree, but perhaps for other reasons than is obvious.