A few things to separate out here---all of these numbers are pretty crude ways to capture some features of the sun-ionosphere system. The sunspot number is kept because there is a long historical record of sunspot counting observations. Later, it was found that the 10.7-cm radio flux (eventually SFI) was a convenient proxy for sunspot number that was easier to collect. Plus, even when there were few sunspots, the SFI varied. It seemed that SFI also had a better bearing on things like the maximum usable frequency (MUF) estimates that HF users wanted. So, that was adpoted. For the past decade or two, we now have solar extreme ultraviolet observations that tell us the relative intensities of the actual wavelengths of ionizing radiation that create the ionosphere. It turns out that especially for low solar activity, the 10.7-cm flux bottoms out and the EUV keeps dropping. So, the EUV is a better indicator of what the ionosphere is going to do. All of that said, for the kinds of things that hams do, the SFI seems to be pretty good and probably better than the sunspot number alone.
A and K are actually indications of geomagnetic activity more so than noise levels. Geomagnetic storms are often associated with processes that cause absorption of HF signals. For example, most paths from the U.S. to Europe pass through the auroral region, especially when it has expanded equatorward during periods of geomagnetic activity. This increases absorption on those paths.