As others have mentioned, we always have to rely on others. Be it maintenance doing their job correctly (not all always do), be it cabin crew, or deicing crews. All of those are (hopefully) well trained professionals and we do have to rely on them. And yes, deicing with running engines, often right next to the runway, is nowadays the norm, has been for a long time in the area i operate in. Additionally, there is of course the thing with the holdover times, getting out of the plane, do a leisurely walk around, organizing stairs to the wing and stabilizer, climbing up there and check myself and then climbing back into the flightdeck, do the last bit of checklists and briefing and then the normal sequence would most likely violate the holdover times, especially in precipitation.
In this case i am very happy that a professional cabin crew and a professional flight deck worked as they should and assured a safe course of action.