Thanks all for the feedback.
I am in the process of adding silkscreen-silkscreen checking. I will also consider text rotation checking. Both of these were outside my original scope which was to ensure that silkscreen was clear of soldermask.
To answer Tolstoy's second request, the utility checks for silkscreen over soldermask pads on pins and vias (if you select these options). Does this not work for you? Or do you want a check for silkscreen over pads that do not have soldermask pads? I can see that this might be useful if you do not use soldermask but do you really have boards like that? Flex?