Tags are more flexible than folders. An actual index let's you search by tag. Folders don't let you search for all photos of your mother, or in 1987, or in Alabama, or some combination thereof.
Folders are a limiting api and we shouldn't limit ourselves to strictly hierarchical organizational structures for non hierarchal data.
I know, but folders work perfectly fine even up to a few thousand files. It doesn't take me long to find a vacation picture from 1966, for example. I look in the 1966 folder, which doesn't have a lot in it. The preview thumbnails from file explorer quickly let me hone in.
It'd take me far more time to set up a proper tag database than I'd save looking things up.
It's still infinitely better than a random shoebox with random snapshots in it.
Looking up something by its clustered index is indeed pretty easy. That's not the only access pattern into most data sets, which is where tags can be handy.
I agree with your last two points, as my family's digital photos are also stored in a fairly similar clustered index style where you have to know the date at least pretty closely to start your search unless you want to scan "all Thanksgivings" [which itself is just a series of clustered index lookups]
Folders are a limiting api and we shouldn't limit ourselves to strictly hierarchical organizational structures for non hierarchal data.