When you buy a ticket for international travel, a large (sometimes huge!) portion of the total price is taxes and fees. You pay those even if you are redeeming your "award" miles.
I suspect it might not be wifely know, but In some cases those fees can be different for kids (even those flying with their own seat, and a full ticket). It is the case for travels to UK.
When you travel to UK, among other fees, there is a fee called:
AIR PASSENGER DUTY (APD) (UNITED KINGDOM) $99.10 USD.
For children, it should be exactly zero.

However, when you buy a ticket on aa.com with award miles, the website fails to recognize that. Recently, I was buying such a ticket,. Even when I called AA on the phone, it took some time to convince the CSR that this fee should be zero for a child (and I spoke with two, both had to consult with their supervisors), which suggests that AA ticket agents are not aware of it either, and it is not properly programmed in their system.
(I just checked, - and with the tickets paid with money, this is done correctly.)

I am guessing that US-UK family travel using award miles is frequent (there is a large number of flights from several US airports to UK). You can imagine, how much AA.com overcharges passengers with kids on a regular basis!

AFAIK I know, until very recently (for quite long time, as compared to, say, UA), AA.com didn't have much (if at all) distinction between children and adult passengers, so there were no differences between adult and kids fares (and in some cases you had to call to purchase a ticket for a kid). I just checked, and on the same route, AA.com correctly quotes lower children fare (and the absence of this fee). But in case of award travel, the website still struggles.