If Kodak was in the "business of capturing memories", they wouldn't have dropped the technology for digital cameras. They wouldn't have been afraid of their own new tech (Kodak had digital camera technology in the early 70s) cannibalizing old tech (film), and instead invested in that segment.
They wasted something like 25 years dragging their heels because they didn't realize that people don't use film because film is somehow magic. They use it to capture memories. Kodak missed that boat, spectacularly, because they believed they were in the film business. Their answer to digital, for a long time, was "let's market film harder"
(Sidebar: For somebody from outside the US, 100 years is at best a mid-term success story. )
So they would have invested a lot in digital cameras, executed well(?) and gone bankrupt. Mobile phones ended up eating cameras for all but very niche uses.
They'd probably become a pretty big fab outside of just making smartphone sensors. The business of memory would abstract into the business of information in general.
So, at that point they'd be in the camera business, sort of. Right? Funnily enough the real long term, not changing thing is: people want to be able to 'capture' light....
You do realize that the long-term success of a company requires more than one decision, right?
SD cards are currently a $8bn market. Phone image sensors are a $15bn market. Digital camera market is $8bn (and growing, fwiw)
There's also the fact that memories need displaying. I hear OLEDs are popular these days. Kodak did groundbreaking research there too.
There were plenty of ways forward for Kodak that still would've fundamentally kept them in the "capturing images & memories" business without majorly contorting themselves. Instead, they were afraid of cannibalizing their own business. (Their really a canonical example in this area). It's Christensen's "Innovators dilemma".
Yes, the real story is more complex than that one decision, or even a handful decisions. There are other splendidly boneheaded decisions that have nothing todo with "capturing memories", but still a lot with "capturing images" - my favorite is that Kodak, shortly before the Boomer retirement wave, decided "eh, who needs medical imaging" and sold that unit off - but the motivation was the same. They didn't want to move from analog to digital.
And yes, getting these decisions alone wouldn't have been an automatic success - but it would have made further success possible. (One of the major things they would've needed to tackle is that analog is chemical engineers, and digital mostly isn't)
But with all these caveats, the root cause for Kodak's demise is still staying strong to a specific product instead of a bigger mission.
That was just one example of what the mission could have been. What should the mission have been?
My point is everyone can say they are betting on a non-changing thing and in retrospect it's easy to see what it could have been (in this case one of several, different ones). You've even expanded on "capturing memories" to make it "capturing images and memories" despite the fact they often have nothing to do with each other (medical imaging isn't related to memories, and diaries aren't related to images).
So what do they do? Go for the most abstract (read: big) mission possible? Why not "we are focused on making people happy". It doesn't change. People want and pay money for it.
Digital cameras were really only viable from ~2000-2010. Kodak might have been able to move those boundaries a bit, but you need mass adoption of fast enough computers and cheap enough flash, and the smartphones killed digital point-and-shoots by 2010.
They wasted something like 25 years dragging their heels because they didn't realize that people don't use film because film is somehow magic. They use it to capture memories. Kodak missed that boat, spectacularly, because they believed they were in the film business. Their answer to digital, for a long time, was "let's market film harder"
(Sidebar: For somebody from outside the US, 100 years is at best a mid-term success story. )