Performance penalty for using thousands of tables in MySQL Background
I'm using WordPress multisite in which each user will have a separate blog. For each blog, additional 15 tables are created. The website will be used by thousands of users. That means that there will be over 15,000 tables which will grow with each user.
Questions

Is there a performance penalty for having this many tables on a single database?
How significant it is compared to a single WordPress installation?
Some day WP will realize that their design of 1 database per user has a scaling problem.  1 user versus 100 users is probably not much difference.  1K-10K begins to show pain, depending on how many are 'active'.

1000 databases means 1000 subdirectories in the filesystem.  That is some burden in the OS.  (10K would be worse.)

15K tables may or may not be an issue.  If, say, 100 blogs are active, then, 1500 tables are active.  That means that you should probably have table_open_cache set to about 1500.  (Plus other settings may need raising.)

But... If you don't have symptoms of performance problems, don't worry.  Perhaps your users are so light-weight that it is not a problem.