The typical, general-purpose binocular is 8x42 because its a balance of weight, objective lens size (in other words low light performance), and magnification. 8x magnification also doesn't have issues with hand shaking. 10x magnification has something of a problem with hand shaking, so usually, 8x is recommended over 10x for people who are new to binos.
Another thing is glass clarity. What I notice often is that people go for higher magnification on lower end optics in exchange for glass quality. They save money by buying lower quality glass and compensate by buying too much magnification.
When hiking, you're going to be tired, sweaty, possibly hungry/thirty, and either standing up or sitting outside in the elements. Meaning, your hands are going to shake more than if you're in a cabin or sporting goods store. So, if you notice shaking being a problem indoors and when you're relaxed, it'll become more of a problem when you're tired.
While eye strain would be a problem if you use an 8x set of binos for a long time, if you're just looking at peaks and the surrounding land, you're probably not going to be glassing for long. And you can just put the binos down. So, I wouldn't worry about straining your eyes by using a lower magnification binocular to look at something.