If by soft you mean the "classical" alloy with 12% nickel, that stuff is so noodly it really doesn't matter. You can literally tie it into knots with your bare hands. I used it on just one guitar and throw away the rest, never again. A professional player can return for a recrown in just 6 months, no thanks. Even the much stiffer 18% can wear fast with intensive use so a few years ago I switched to EVo wire which is again harder and stiffer. It went OK on new boards but when refretting, if the wood is soft or too chewed in the slot you can have a hard time making it seat. Even on a new guitar it can be troublesome beyond the 12th. A few times I couldn't make them go in fully no matter how much I dared to hammer so in the end had to do a serious amount of filing and recrowning.
Stainless is again tougher than evo but I didn't notice any extra issues hammering it compared to evo. it is definitely a pain to cut and file so now I do must of this work on a grinder, including the bevels.
I have pressed only once, with evo. Worked very nicely but since I had an improvised press made from a screw clamp, it took a long while compared to hammering.
Last job with hammered straightened evo went really well with zero sweat and cursing beyond the 12th, and this is a very wide 8 string guitar! I am very pleased.
Either hammering or pressing, you are exerting an amount of force/stress on the metal, and on the wood from the barbs. Some of this energy needs to straighten a curved wire, or at least hold it in tension with the barbs. So I can't imagine any benefit from using curved wire.