With social-distancing measures being implemented in many countries I would expect other viruses, like the ones that cause seasonal flus, to have also a hard time propagating in these circumstances. Are there any estimates or research (epidemiological models) I can check, about the possibility we are winning by accident a war against many other less alarming viruses?
Yes, this helps as well with other infectious diseases. A good example is the flu, which season was measurably shorter this year than in other years on record. See the figure from the reference 1 for comparision:
Reference 2 shows that this is also true for other respiratory diseases (figure 2):
This shows very well that the isolation measures and the social distancing work very well to control such transmissable diseases.
In addition to Chris' answer above, the effect is even more pronounced in Southern Hemisphere countries where flu season started during the pandemic. The New Zealand lockdown and health response dramatically lowered the prevalence of reported flu-like symptoms.