To begin with, I'm not talking about merely washing away a virus with soap (and water), but rather that enveloped viruses, like influenza appear to also be directly attacked in their lipid envelope by soap compounds, as a 2018 paper studied:
An influenza epidemic is still a problem despite the development of vaccines and anti-influenza drugs. Preventive measures such as handwashing are fundamental and important for counteracting influenza virus infection. In this study, we clarified the anti-influenza virus effects of surfactants, which are the main components of hand soaps for hand washing: potassium oleate (C18:1), sodium laureth sulfate (LES) and sodium lauryl sulfate (SDS). For a human influenza virus strain (H3N2), C18:1 reduced the infectivity by 4 logs or more, whereas LES and SDS reduced the infectivity by 1 log or less. Similar results were obtained when an avian influenza virus strain (H5N3) was used. The interaction between the surfactant and virus was then investigated by isothermal titration calorimetry. The LES-virus system showed a positive value of enthalpy changes (ΔH), meaning an exothermic interaction that indicated a hydrophobic interaction. In contrast, both the C18:1-virus system and the SDS-virus system showed negative values of ΔH, meaning an endothermic interaction that indicated an electrical interaction. The ΔH value of the C18:1-virus system was much higher than that of the SDS-virus system. A mixture of C18:1 and HA proteins similarly showed negative values of ΔH. These results indicate that influenza virus inactivation by a hydrophobic interaction of a surfactant with the viral envelope is insufficient to prevent infection, whereas inactivation by an electrical interaction of a surfactant with HA proteins is sufficient to prevent influenza virus infection.
Alas the abstract of this paper (by Japanese authors) is rather... abstract/technical. By which I mean I can't immediately tell e.g. how effective (the various) soap compounds are relative to typical antiseptics (like alcohol, chlorhexidine, iodopovidone etc.) in inactivating enveloped viruses. The paper quoted above does compare these soap compounds against each other in this regard, and potassium oleate (C18:1) seems the most important compound as far direct inactivation goes. (The [log] infectivity reduction figures mentioned are apparently after a 3 minute "intubation" experiment at room temperature, if I read the methods section correctly.)
But, is there a direct comparison of the speed of inactivation of enveloped viruses in a soap solution vs antiseptics published somewhere else, or can it at least be inferred from the data on soap form this paper? (This paper has only 1 citation in Google Scholar, so apparently not a very exciting topic... Also, it was sponsored by a soap company.)
I see another (2019) paper from Japanese authors cast doubt on the effectiveness of alcohol against enveloped viruses... although this latter study also involved (ahem) mucus as an extra protective layer for the virus.
In a series of tests, the researchers from the Kyoto Profectural University of Medicine found that ethanol-based disinfectants, or hand sanitizers, would have be in contact for at least 4 minutes with the influenza A virus before killing it, a much longer duration than typical use. After 2 minutes of use, the virus was still active. [...]
The reason ethanol-based disinfectants might not be as useful as previously thought has to do with the mucus that surrounds droplets of the influenza A virus. The mucus acts as a hydrogel and protects the virus from the ethanol, the investigators reported.
So that makes the issue/question of comparison of inactivation speeds on enveloped viruses (e.g. soap vs alcohol) perhaps even more interesting.