>Maybe the smart play when faced with a barrage of arrows is to close the distance as quickly as possible
and that is where volley may be helpful - simultaneous hit to multiple horses and soldiers may break the pace and may cause stumbling and local pile-ups. Slow down of advance -> more exposure time to the follow up arrows.
It takes a special (in a bad way) kind of commander to send more arrows after their cavalry and infantry engaged. I'm sure there are records of it having happened, but you have to assume you're taking just as many casualties as the enemy due to friendly fire.
The anti-cavalry arrows are never sent after engagement, any more than commanders on the front line today call for indiscrimenent shelling on their own front line.
Anti-cav arrows were used at Agincourt to great effect, although it's possible the mud killed more French than the English did.
I assume the accuracy of the average arrow and non-professional soldier might dissuade one to get anywhere near the fire range. Enough will fail to launch properly, slip or be dysfunctional that there's no way you'd want them shot from right behind you.
Eh, plenty of people run into the line of fire even today. People don’t think straight when under a lot of stress.
Also, the only safe place to be in War is far from it; so by definition soldiers need to be trained to ignore a lot of threats to their wellbeing in order to do their job.
and that is where volley may be helpful - simultaneous hit to multiple horses and soldiers may break the pace and may cause stumbling and local pile-ups. Slow down of advance -> more exposure time to the follow up arrows.