Why? Because we don't have access to any databases. I dread to think of the requests and committees I would need to find and traverse to get a database set up for my team, let alone a system that I can write and run code on. Yet we can guarantee that every internal and external user has access to Excel.
Unless you are working for a software firm, or are part of a dedicated analytics team with access to suitable systems, large companies and government pretty much have no chance of being able to roll your own database.
Don't suggest Access. Never suggest Access.
Can you try sqlite? It's usually enough for simple things I think.
So Excel > PostrGRE? :)
I wonder what kind of data did you use and why it had to be stored in so many columns. This approach would probably kill a "real" database too.
With a relational database this would be kind of insane, as it's much easier to normalize data into separate tables, then just join up them up when you need to.
Because of that, chances are the natural format for a data item taking 16,384 columns in excel likely takes fewer than 16,000 columns in PostreSQL.
From my experience these monstrosities are usually created by two reasons: Push from business side and a data team too slow to react. Thus the analysts have to create the first version that seems to be OK and smart but eventually evolved into a monstrosity.