I suffer this now with several financial sites. Whilst I agree in principle with the criticisms you, LP, have made about sites taking this approach, and have complained, it seems unlikely that these institutions are going to shift easily and in the meantime, I have to suffer.
It is worth pointing out that, in my case at least, this random character stuff is only one part of their "security" as they also ask for a passphrase and sometime a code generated from whatever additional device I have to carry around.
Therefore, I really really would like to see you add a feature to be able to quickly copy the nth character from the password without having to reveal them to observers or making me count character positions. (Actually, one site requires me to select the correct character on a drop down rather than pasting it in, so I do need to reveal the nth character in my password then so I know what to select.)