(1) She had done what God asked of her.
(2) I inquired of them the score.
(Examples are from COCA)
I can guess from NED (III.10.b) that when you use ‘ask’ or ‘inquire,’ construed with ‘of,’ you should regard that something you ask or inquire are acquired from of’s complement. For example (2), you expected the score would come out of them. But the trace, in the past you used ‘at’ instead of ‘of’ for both ask and inquire, makes you think of-complement as both your seeking orientation and whence the result comes. Is this how you think when you use ‘ask’ or ‘inquire’?