You're not alone for wondering.
Matter of fact, not only on this board but many of my friends/associates in RL feel the same way, since most of the benefits derived from Amex (save for a few) can all be had from other issuers at a lower price.
In my view, I find their credit products to be a very good fit for most people, especially the Blue line of cards. They represent an excellent balance between rewards and cost. Good examples would be the BCP and SPG. I can't imagine anyone who wouldn't derive benefit from the BCE--no fee, revolving, Amex proetection, 3% cashback in supermarkets, etc...
It's the charge cards that either are great, or not. There is very little middle ground. The appeal of the charge card are for those who are relatively indifferent to credit scoring (or, may not have the highest or most pristine Fico scores), but prefer a product that focuses primarily on spending ability and income stream rather than the objective scoring models.
In general (there are always exceptions, of course), those who prefer the no-fee Amex revolving cards believe in a "fair and objective" scoring system which doesn't emphasize income stream--the deomocratization of credit. It keeps things such as bias and unfair demographic profiling out of the equation. While Charge cards are more of an "old world" product where income stream is more important than the "objective" credit score. For most of Amex's history, the charge cards were targetted to those with the ability to spend or have high incomes while excluding those with lower spending thresholds irrespective of any fair & objective credit scoring model.
I suspect how you feel about the value of Amex will be predicated somewhat along these lines.
Case in point. If you happen to spend and fit the criteria Amex prefers, there's almost nothing the company won't do to accomodate you. Unlike other issuers who reserve some of their best perks for new customers, Amex reserves some of the best offerings for existing cardmembers. It's a formula they use, but it appears they take account the value of one's membership date (even CSR reps) more so than other issuers.
Finally, the backdating for a member since 80s or 90s is priceless. With a membership backdating 20 years, applying for a new Amex every January completely neutralizes a new TLs adverse affects on aaoa.
