You can really go down the rabbit hole as to what an AA mile is worth when you look at this sort of thing.
And there are two sides to the equation: earning and redeeming.

Most travel pundits and those in the points game put an AA mile at a value of an average of 1.6 CPM. I would tend to agree, given the overall program / award availability and pricing / ability to rack up miles.
On non-bonused spending, you are earning just 1 mile per dollar on CC spend. The bonus for certain spending categories (up to 2 or 3 miles per $) can help increase your average mile per $ on CC spending. So maybe your blended average is 1.2 or 1.4 CPM, at the end of the month on your statement?
Comparing that to a 2% cash back card though, you may find yourself cringing at the opportunity cost - missing out on (in essence) ~0.5% cash back.
Now add in the shopping portals, earning from actual flying, etc. - your ability to rack up miles (and potential future value) via other avenues is far greater than what is available with a comparative cash back card only approach.

However, where AA miles can shine is by excising a good value out of them when redeeming.
Any redemption north of 1.8 cpm is "good" in my book.
Anything north of 2.5 cpm is what I consider a very good value.
Anything less than 1.5 should be treated as an equivalent to the cash fare.

Recent data point:
Just booked LAX-SCL for Nov23.
Outbound cash fare was $4.5k for one way J. Got it on miles for 130K miles. Comes out to 3.46 CPM - an excellent value.
Return cash fare was $1.3K for one-way J. Miles cost was 130K. A presented value of just 1 CPM - not so hot.
I opted to use my stash of Chase Points, and was able to get the same $1.3K fare via the Chase Portal. No out of pocket cost and now I can earn RDM and LP on the ticket as well!

But, the big caveat to all this is that AA miles are inherently more susceptible to inflationary pressures and the dreaded devaluation.
The miles aren't accruing interest in your account, unlike cash back rewards would. So better to use them now at a respectable (but perhaps not all star) redemption rate, rather than stack the chips high hoping for some extreme great value redemption in the future while they take the hit of annual devaluations and program changes.

I like AA miles overall as an award travel tool, but I have become less brand loyal when it comes to CC spending and earning rewards in that manner. I spread the love there between AA as well as Chase points, Cap1, and WF cash back.