Two types of websites would be good after you die:
The first is obvious-Your website makes a profit, and you want your family members to continue to profit in your absence. This is kinda like how life insurance works.
Put ownership in your will and credentials in a safe deposit box! If you make a substantial profit, you should probably register as a business and put a succession plan in place.
The second type is for spiritual types like me- I believe in an after life, and I want people to have faith in Jesus. I might not meet you personally in this life, but if I helped your faith, it'd be cool to know you later. I'm not one who gets in arguments about what is the minimum for salvation, or what the minimum you need to do to get to Heaven. But I know it stokes God when we follow him, do good, be loving, and help people in their faith. So helping people to find Jesus even when I'm not around will be beneficial.
I, too, believe in the afterlife, but I'm not sure I'd want an eternal website trying to convert people to my chosen faith. Most sects and denominations already have websites; maybe you could share your testimony on one of them (providing them permission to host your comments even after you die).
I run a website which I think should be perpetuated long after I leave this mortal existence, but it doesn't match either of your two categories. I host the largest genealogical sites for my surname. Indeed, I am contacted daily to verify information on other sites. I want those photos from the 1800s to be available a hundred years from now. I want my descendants to know why I believe a certain family story is false. I want to preserve family stories I have verified as true (including teaching a French princess English).