Ive done quite a bit of mountain climbing. Well ot be honest more ski mountaineering than mountain climbing cause i would rather ski down then walk down.
Ive done plenty of smaller peaks around WA in the Olympics and Mount Rainier (well by small as in not mt. rainier or mt. baker). Plus done Mt. Baker.
Honestly the biggest danger for probably 75% of climbers are crevasses. Followed by falls. Falling down a icy slope can have you sliding thousands of feet. Weather is the third biggest danger for those 75% of people IMO. If you dont plan it out it can be devastating. But planning and an understanding of weather patterns can really help with that. The first two can be solved by using harnesses, crampons, ropes, and ice axes. If one person falls into a crevasse or just falls, the aim is the other climbers and arrest and stop the fall. Weather is just being smart.
For those who ski down (and also those who climb early season and late season or in winter) there are other factors. Avalanches come into play, wet slides, and the conditions. if its super icy then skiing down can be incredibly hard and dangerous. Plus things like rollovers (big avy spot), narrow entrances and exits, ect are more things to consider. When its mid summer stopping on a rollover isnt that big of a deal but in early spring its a good spot for an avy to occur.
The third are those who do a lot more technical climbs. Rappels, needing anchors, climbing ice falls, ect add more to a climb and require knowledge and skill.
Honestly though pretty much any of the major mountains (ie shasta, baker, whitney, rainier, hood) are just hard walks up a big hill. Only in the sense that the danger is pretty low when you stay on the main routes. (going a less common route is harder for sure) There are usually boot packs already in place to follow, crevasses are often marked, and you often have people around to help if SHTF. Obviously theres a bit more to it as you need a basic understanding of crampons and ice axes on some routes but you dont need to be an expert or anything.
As a guy ive climbed with before said "its only as dangerous as you allow it to be"