I know folks who never take an ice axe but rather when they solo, take trecking poles. The reason being that 3 points in contact with the ground is better than 2. When faced with a tricky situation he simply slowes down and makes very sure firm placements. He does wear boots though. He does glaciers routinely this way. Though I still think he is certifiable in that regard on large glaciers. I did get him to buy a BD whippet reently and he even admitted that he used it once, otherwise I would have been going to his funeral.
I know others that when going up Denali take a trecking pole and a long ice axe. They got away with this because they knew that fixed ropes were in place. Once again 3 contact points is better than 2.
I honestly cannot remember the last time I cut a step(mainly because I typically take and or wear boots/gaitors/crampons when mountaineering). I think it was about 15 years ago when faced with a newbie group, a hard iced snow filled chute across a trail, and a very bad scree field below if one slipped as everyone in the group had tennis shoes on. This was trail walking. 90% of what most folks do. For the 90% factor, most would gladly take the aluminum axe. Especially as you live on the east coast and will be doing most of your hiking out there. Though if you want to do winter stuff... We aren't talking much weight here.
Comes down to, buy 1 "heavier" piece of gear, or buy 2 for different applications. Most can't afford to buy 2 pieces of gear(myself included).