Lots of other people have mentioned very good practical reasons (and you can read the linked post for others, like people being unsure of what the password to the Vim FTP is), but there are lots of good sentimental ones as well.

When something like this happens, you lose your mind slightly, and you become obsessed with preserving whatever is possible to preserve of the person. I went so far as to record his voice-mail message, just because I felt i needed to.

Of all the internet stuff, the thing that was most important to us was photos: he was a photographer, and he used a photo-uploading service (I think it was Google Photos, but I'm unsure, it's been a couple of years) and I was able to get an archive with all his thousands of photographs.

Eventually, I put everything I could possibly find (computers, internet services, whatever) into one big zip file, and put it on my local NAS (which is backed up to the cloud). I don't think I'll ever have the heart to go through it again, but my brother had young kids who never really got to know their dad. I figure one day they might want to look at it (even if it's 30 years from now) so it makes me feel good to know that it's been preserved.

When my father in law passed away his wife asked me to get some photos on a thumb drive for her. I knew his password from watching him login, I also went ahead and deleted his browser history.

If you are perfectly prepared for your passing and made your will, arranged all the financial stuffs, told your friends and family everything needed etc. then you don't need to give access to your accounts. But many people don't have that luxury. When death is unexpected, things get messy, e.g you may want to continue paying the mortgage on time, or shutdown social media accounts, or make announcement of their passing using those accounts, or contact their lawyer, or cancel subscribed services, and so on.

Being able to unsubscribe to a service, as someone else mentioned.

In social media world, posting some final "xyz has passed on. this account will be closing" or similar 'wrap up' activity is often useful.

While most people have focused on post-mortem account recovery, that's not the only occasion. The small company I've worked for has had the last three administrators leave the company in arrears for a time with quick departures and little handoff of procedures. It is all the more frustrating because we overtly use a shared password managment tool for accessing client servers.

When my dad died my mom needed access to all the accounts to do things like pay the electric bill. That is all done online so without him logging into the online bill pay she would have no way to know what was owed. I suppose after a few months of not paying they would send a paper bill, but then there are late fees and the like.

Anything with recurring billing needs to be cancelled, for a start.