This is a lot more complex than just a software-selectable forwarding option - and is true not only for Cisco but most other vendors.
First of all - store-and-forward vs cut-through generally isn't software selectable on most switches. It's potentially available if the speeds of ingress and egress ports are equivalent but as soon as multiple speeds are involved (say 10G -> 1G, for example) then store-and-forward isn't an option but rather a basic necessity.
The entire premise of cut-through is that the switch doesn't need to wait for the entire frame to arrive but rather as soon as the destination of the frame is determined (..within the first few dozen bytes received) the frame is immediately copied to the output port. This is to say that the output port is transmitting while the receive port is still receiving. In the case of a mismatch of speeds this literally isn't possible, as the bits arriving on a 1G port aren't clocked quickly enough to be pushed out at 10G (and, similarly, need to be buffered in the other direction).
In contrast, store-and-forward means that a given switch needs to receive the entire frame before it's transmitted. This necessarily means that each switch incurs enough time for the frame to be de-serialized, processed and re-serialized. It also means that packets with errors can be dropped and other kinds of processing can be achieved. There are actually some other wins in this kind of approach as far as prioritization and certain kinds of fancy forwarding are concerned.
I don't know fragment-free refers to. There isn't really a notion of fragmentation in L2 switching. I've heard of various mechanisms of memory management concerned with fragmentation management but it's not directly applicable to the traditional s-and-f vs cut-through discussion.
To your last question - the lowest-latency switches out there tend to run fairly light buffers and fully symmetrical bandwidth which allows for the box to have as little processing (read: latency) as possible. This is true for both the Ethernet world as well as Infiniband.
The thing is that maps pretty well to the spines of spine-and-leaf designs but starts to break down when applied to the traditional requirements of actual at-scale networks in the real-world (read: 2-3 orders of bandwidth, ranging from 100M/1G/10G/25G at the edge to 10G/40G/50G at aggregation and 40/50/100G at the core). Put another way - good for spines, bad for leaves, worse for traditional networks.
The performance of store-and-forward is absolutely improving and the truth is that some switches can actually operate in a hybrid mode but store-and-forward is still pretty much overwhelmingly common. Faster memory and advances in bus design have absolutely contributed to this improvement but it's important to note that many of these improvements asymptotic and are tied to improvements in IC fabrication scale and, ultimately, physics (thus the oft-promised push for silicon photonics).