For me, it was a matter of convenience, although cost was a big factor as well.
Acetylene isn't the best choice for melting platinum metals due to the excessive carbon molecules in the gas. Natural gas burns clean, virtually impossible to create a smoky atmosphere, very unlike acetylene. However, it should be noted that a controlled atmosphere furnace can carburize, so it's obvious that there can be free carbon. Aside from an induction furnace, the next best choice would be a hydrogen torch for melting the platinum metals.
Melting with natural gas has limitations. I could melt a little more than an ounce of platinum, and even that wasn't easy. I am not privy to the temperature of the flame, but it must be considerably cooler than oxy/acet, which is reputed to be in excess of 6,000°F.
For gold, however, which melts at roughly 1,300° lower temperature than platinum, it was a natural. Never had to worry about running out of fuel, and I kept a spare oxygen bottle at the ready. I was never inconvenienced by running out of fuel in my more than 20 years of operation. Significant in that my torch was in use daily.
I recommend natural gas above all other fuel sources, assuming you have it at your disposal. It's clean, cheap and user friendly. Lighter than air, so it can escape, unlike propane.
While I don't have numbers, there's no question, propane is far less expensive than acetylene. Stands to reason considering calcium carbide from which acetylene is made, is a man made product. We must make a product to convert to a second product in order to achieve the end goal. It is also a very unstable gas, readily self ignites (violently) when under more than about 15 psi. To avoid that problem, it is dissolved in acetone in cylinders. Note that there's a red line on acetylene gauges.
Harold