That's not the reason.
Alkaline batteries only have 1.5V for a short time. In practice, toys are designed to opeerate off of 1V to 1.5V, because Alkalines vary _wildly_ in voltage during use.
NiMH at 1.2V _STAYS_ at 1.2V, even when drawing 1Amp or more (under these conditions, Alkaline would have long dropped below 1V).
EDIT: This is also a problem because "nicer toys" will measure the voltage assuming an Alkaline is "full" at 1.5V and dies at 1.0V. However, NiMH starts at 1.35V, then "plateau" at 1.2V, and stays there for most of its life, before rapidly falling off to 1.0V or .8V like a cliff at the end of its life. So NiMH life "cannot be predicted" by any simple metric.
I had an issue with the original Apple Magic Mouse that would not work correctly with NiMH batteries but work fine with disposable AA. The mouse would be fine for a few days then randomly stop working; using fresh NiMH would revive it again. I assumed it was due to 1.2v vs 1.5v but perhaps that particular mouse (or all Magic Mice) was just bad.