For us, it depends on if we know we have a repeat job or not. If not, it often isn’t worth the extra time to make the jaws fancy.
If it is not or we do not know if it will be a repeating job, typically the operator will mount the jaws. The pickup will typically be the center of the back jaw for X0, center between the jaws for Y0, and top of the jaws for Z0. They will be instructed to clamp the jaws while spaced a given value apart, and also given the depth of the pocket and size.
Most soft jaws we make are for round parts, so if the jaws are not cut up for another usage, they are relatively easy to align - leave both jaws loose, eyeball the jaws aligned and then clamp a part. You can then tighten the mounting screws and the jaws should be aligned correctly.
If it is a repeat job, we try to make the front jaw more mobile, IE not required to be aligned any certain way with the back jaw, where possible. Typically we will then come off the left edge and front face of the back jaw for XY0, as that is a quicker pickup than center. We use the same pickup to machine the jaw as well.
An alternative to that may be a datum hole, as previously mentioned. I prefer the front/left corner of the back jaw myself, but an interpolated datum hole in the jaw could be more accurate.
My preference for round parts is actually to use hard vee jaws where possible - you have the same time in swapping jaws but you don’t (potentially) burn $10 of jaws and labor every time you need to hold a round part.
But for repeatability and ease of use, cutting a counterbore for the part to sit on is best, especially if there are several parts - no worries about the part not sitting straight in the vee…
If you have a thin ledge on a cylindrical part you can relieve your jaws with a t-slot cutter or similar if there is a more substantial diameter to clamp on.
Holding multiple parts is easy (for round parts) IF you have good process control on your round parts. We have a job coming up, a repeat job, of 220 pins with 8mm diameter stems. With one set of jaws I can hold 6 at a time for the mill up (facing thickness, milling a flat and cutting three counterbored holes). Like any “high-density fixture” it saves a ton of time in tool changes and rapid moves.
For flat parts I don’t really recommend holding multiple parts… at the most, hold one part on the left end and one part on the right end of the vise. And really, it don’t have to be soft jaws for this. Any more and you run a risk of clamping some parts tight and others not. It can be done - but there is an inherent risk.
A well-made soft jaw, blown out correctly, should not mark an aluminum, brass, steel or harder part… plastic might be different. But if you have matching contours, it should make the pressure even around the perimeter.