MySQL - Is it good to have millions of tables in a single database?
Absolutely not.

Each table takes at least one file in the directory that represents the database.  The OS overhead is non-trivial.  The OS effort to find a single file (table) in a million-file directory is not pleasant.  Etc.

If it generally poor design to be dynamically creating tables; it is terrible design to be creating millions.

Millions, even billions, of rows in a table -- this is OK.  Having an extra column that replaces your "table" designation -- this is the "right" alternative.

If you would like to discuss your application further (and more specifically than "parent" and "column"), we can discuss other design considerations.

Same arguments apply to having millions of databases.