Our issue revolvers were attached to our persons by a lanyard, whilst also being in a side holster. This was for "Dress" Uniform only. We did not wear the lanyard when on duty, but still had the flap-over-the-grip holster. I assume both the lanyard and holster flaps were to prevent loss while on horseback. That is something I never got to experience while working (riding horses) and obviously were 19h century holdovers.
Some things change slowly.