Most modern cases (that are any good) have custom made mounting fixings. But vibration can be an issue and some user ingenuity is required:
Including but not limited to using various forms of packing to suppress vibration. (Some people like things that vibrate) but not me. And it not unknown that I place the PC/Box an a piece of carpet in some situations.
Soft mountings are always preferable. In my case, I can simply suspend HDs on rubber bands and it works well but I’ve returned to rubber grommets because of the possible consequences of forgetting that the HDs are effectively bouncing on a trampoline when I decide to move the case from underneath the desk for surgery…
Consider a floating drive. The reading head is starting a movement toward a track. As it starts forward, the body of the drive starts movement backwards. This shake of the body is transferred to the axle of the platters.
Considering that this happens many times per second, the vibration of the body may induce wear and tear on the platters’ axle’s bearing.
On the other hand, if the body is fixed to heavy and sturdy object like the computer’s case, then there is less vibration of the body and less wear of the bearing.