Does Kicad (pcbnew) allow dragging nodes — i.e. junctions between track segments?
Well, I finally found the answer on my own so I'm posting it here in case someone, just like me, happens to wonder. Put Kicad in OpenGL view mode and drag vias, tracks, track corners or whatever you want — provided you set DRC and routing constraints, of course. It is explained in this video on Youtube.

To drag items while in OpenGL view mode, select Add single track on the rightmost toolbar and then press D over the track/node you want to drag (no click required). The router will shove tracks or move the one you're dragging around according to the routing preferences you previously set. Press E while adding a (single) track to set routing preferences.