> Any particular reason to use a SS braid PTFE instead of a plain PTFE hose?
Ah - slight misunderstanding here. You can't buy PTFE tubing in 1/8" size with SS braid over it (afaik). The smallest you can buy is 1/4". That size is routinely available for fuel injection on cars, but it is very heavy and stiff. It has been used by several stove vendors, but many people have commented that the result makes the stove wiggle around at the end of the hose.
What I was suggesting is that you get the 1/8" PTFE (or FEP or PFA) tubing and sheathe it with some SS braid. I had to buy the SS braid from China, custom made, but you might be able to find something in the USA.
WHY use it? Two reasons, and underlying both of them is the danger from a gas leak. You haven't lived until you have experienced one: extremely dangerous. Paranoia is excellent.
The first reason is to avoid any cuts and other damage. All three plastics are tough in tubing form, but accidents can happen. Note that even PTFE is not immune to melting on a bit of red-hot stove.
The second reason is that having SS braid over the tubing and crimped onto the connections at each end gives a degree of security against the connection failing. The tubing is held in place.