I'm thinking about using RG-316 (RG316) SMA cable assemblies for non-performance-critical applications where I primarily want flexibility and ease of use. Any particular thoughts on this? Any alternatives that people prefer in this flexibility class?
Without knowing your application it’s impossible to conclusively say whether it’s suitable or not. But it’s one of the most common cable types.
RG316 and the thinner RG178 are both PTFE dielectric and FEP jacket. Most of the stiffness comes from the FEP jacket, by the way. In pure theory, you could strip off the jacket and insulate it with something else to get a more flexible cable.
RG174 is cheaper (polyethylene dielectric, PVC jacket) and is usually more flexible, but the flexibility varies wildly by manufacturer. Some cheaper manufacturers use PVC that is WAAAY stiffer than others.

I recommend buying a smaller sample of a given brand before buying a bunch. I can say that Huber+Suhner’s is quite flexible, while the one from Tasker is really stiff.
RG58 is also polyethylene dielectric and PVC jacket, but thicker. So usually stiffer than RG174. (Note that technically, RG58 has a solid conductor, while RG58A/U has a stranded conductor, but many RG58 without suffix are stranded anyway.) RG58A/U is what is most commonly used as the “default” cable for BNC assembles. Since it’s fatter it has generally better performance than the thinner cables.
I use all of these (and RG196, which is RG178 but with a PFA or PTFE jacket, which has superior chemical resistance, temperature range, and high-vacuum performance than FEP) at work, as well as a few others. Really depends on what your needs are.
There is also RG188, which is very similar to RG174 and RG316, but with PTFE dielectric and PTFE or PFA jacket, so the same mechanical/environmental advantages as RG196.
There exist extra-flexible coax cables like Stäubli’s SILISHIELD cable which is basically RG58, but uses silicone for both the dielectric and jacket and extraordinarily finely stranded wire, but at the cost of the impedance being 45 ohms instead of 50. Stäubli also makes a regular PE/PVC RG58 with a fairly fine stranded conductor and soft PVC jacket. I haven’t used either of these, but want to try them out.