"He does not insist on one of the usual dreadful concoctions from the physician but treats me as he might a child [...]" (https://www.melissaaddey.com/wp-content/uploads/2018/02/CS-TheConsorts_5x8_print_12-06-2016.pdf) I understand he treats her as he would treat a child, but I am curious as to why there is no verb after "might". Would it be more appropriate to say "[...] treats me as he might treat a child [...]" ?
It's quite normal to omit the repeated verb as in the original sense. (It is perhaps a bit literary; we might not say it that way.) You can also say it your way, of course.