I’ve been using trail running shoes for weighted ME and indeed most of my aerobic training (at least since the snow melted).
I have mountaineering boots, approach shoes and trail running shoes. I use the lightest and most comfortable shoes for the objective – if no need for crampons, no need for mountaineering boots. Similar comments in this thread: https://uphillathlete.com/forums/topic/trekking-poles-and-shoes/