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Virtual RDBMS over SQLite
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> I searched the net and discovered that a database with only 1 table was very popular

It's not very popular at all, and you certainly did not find that on this forum. 

I mean I'm sure you can find examples of people doing it, but that's like saying the act of strapping a Deer to the hood of your car on the drive home after the hunting trip is very popular because you can find many pictures of idiots who did that on the internet. While it is true that you can find many examples/pics of said idiots, it must never be mistaken for popularity with people in general.

I can't speak for all DBs, but for the ones I do use (SQLite, MySQL/MariaDB, Postgres, MSSQL) I can promise you there is no advantage to any DB having one table per schema precisely, as opposed to two or more. In fact, I can point out many disadvantages.

I feel less strongly about the other possible meaning you could have intended, namely that using a set of single-table files is one way of solving a multi-format virtual/object model. Perhaps "also-used-sometimes" is better phrasing than "popular" - plus I still fail to see a significant advantage. [PS: If there is a tangible advantage that can be shown, I'm very willing to be corrected and very interested to hear about it.]