In addition to what has already been said, you can easily insert limit switches into the series of stop buttons to shut down when a certain condition is sensed, but would still need to manually restart it. Doing so with maintained switching scheme would automatically restart when the limit switch returned to normal condition.
Also can put limit switches or aux contacts from other components in series with that holding contact, open any of those switches and the contactor drops out. This may allow for conditions where the start bypasses the holding contact when pressed and your motor starts, but if other items in the series are not in normal operating condition it stops again when you release the start button.
I also run into "automatic restart" needs on some equipment. In particular irrigation systems - the POCO's may remotely shut down your system when total demand is high (they offer better rates if you subscribe to let them do this) to manage load on their system during peak demand periods. Many owners want that system to automatically restart when the POCO allows their system back on line. A simple timed contact parallel to the start button allows restarting, but since it times out and opens again if there is a malfunction in the system it shuts back down. If you held the start closed - most of those systems it bypasses some of the running limits but in this case no one is there to supervise and you don't want the start command to last more then a few seconds if there is a malfunction that a limit has otherwise opened the circuit for.
Multiple control stations - the conventional three way/four way switching circuit works, and uses same number of control conductors, but you don't really know if it is on or off state when there is some other limit switch putting it in an off condition. With momentary start/stop buttons, pressing any stop button will stop it regardless of other conditions, pressing any start button will start it if nothing is locking out the control circuit - like an unsatisfied limit switch or tripped motor overload.
There may be many more individual application examples of why this might be a better control scheme then a simple maintained contact as the primary operator interface.