Mooper - the points you make are VERY valid - It is a sad fact that many people not only for this program, but for many others - simply do not value their time perhaps the way you or I do.
There are only 2 benefits to this program that I can see:
1 - Quick way to meet minimum spend thresholds. Is it worth time hassle and risk for 750 AA miles - NO WAY !! Is it worth it for 25,750 miles - I would say YES.
So for those who do find it difficult to spend $750 in a 60 day period per card (and if you are doing this for husband and wife thats 2 cards each = $3000 in a 60 day period) then this US Mint thing helps.
2 - Meet other minimum requirements (like to gain a certain status) or perhaps you need some quick miles to top up an account.
But the thought of getting 20 boxes of coins - having to track them - the worry if they get all delivered - and then dragging them to my bank - for 5000 AA miles/SPG points or whatever, is simply not worth it to me personally. My time is far more valuable.
But to each his own - like some have said - they LOVE the buzz of collecting miles