By my way of thinking (and I believe OSHA's, too), Emergency Stop is purely a safety device and it means just that: Stop for an Emergency! Do It Now! It should ONLY be used for emergency purposes.
It is debatable as to whether things like regenerative braking should or should not be used or whether nip rolls and the like should be powered open or not, but that is another question all together.
So anyway, when an E-stop is used I don't care too much about mechanical stress, unless of course this in itself creates a new safety hazard. Such issues absolutely must be taken into account during the machine design so that and E-stop can be safely provided. If they are not, then it is a poor design and one that should not be accepted. Period. No ifs, ands, or buts.
For the remainder of my speech, I use large web-handling machinery as my basis of thinking:
Because not all rapid machine stops have to be E-stops, a Rapid Stop can also be incorporated. This type of stop should be labeled just that way and should then incorporate the deceleration you describe. This is usually intended to bring the machine to an orderly halt as rapidly as allowable to maintain as much machine and product integrity as possible. This can be used any time an operator deems it necessary.
Lastly, there is a Normal Stop. This is a stop that allows everything to ramp down together and is the type of stop the Machine operator should normally use. If done well, this type of stop will usually allow the machine to be restarted with minimal setup or operator intervention.
That's my position anyway.
Steve