A convenience-store onigiri can have soft, moist rice and still come with crisp seaweed. The secret is not in the seaweed itself. It is in the packaging.
In a typical triangular onigiri, the rice and nori are not touching when you buy it. A layer of plastic keeps them separate, preventing moisture from the rice from reaching the seaweed. You first pull out the center strip, then remove the two side sections. Once the wrapper is gone, the nori is left wrapped around the rice. The rice and seaweed finally meet only when you are ready to eat.
Nori quickly softens when it absorbs moisture. If it were wrapped around the rice from the beginning and left that way on the shelf, it would gradually lose its crisp texture. The packaging solves that problem by keeping the two apart until the moment the onigiri is opened.
With convenience-store onigiri, many people expect the nori to be crisp. If you opened one and found the seaweed already soft, it would not necessarily taste bad. It would simply feel a little different from what you expected.
At home, the expectation can be different. Nori that has absorbed moisture from the rice and become soft can still taste perfectly good on a homemade onigiri. Japanese people do not generally think that nori must always be crisp.
What changes is the kind of onigiri being eaten. Soft nori feels completely normal on a homemade one, while crisp nori has become part of what people expect from a convenience-store onigiri.
To someone unfamiliar with it, the numbered “1, 2, 3” wrapper can look surprisingly complicated. For many Japanese people, though, it no longer feels complicated at all. They have used it so many times that they usually open it without giving the mechanism much thought. The packaging has simply become part of what a convenience-store onigiri is.