At first access time will appear faster in SQLite
Access time for SQLite will display faster in the first instance, but this is due to the small number of users on the Internet. SQLite uses a very simplified access algorithm, quickly, but does not handle concurrency.
As the database begins to grow, and the amount of concurrent access begins to suffer. The way servers handle multiple requests is completely different and more complex and optimized for high concurrency. For example, SQLite locks the entire table if an update occurs and orders orders.
RDBMS does a lot of extra work that makes them more scalable.
MySQL, for example, will create QUEUE access even with one user, partially block tables, instead of allowing only one time execution by the user and other rather complicated tasks, to make sure that the database is still available for any other simultaneous access.
This will lead to a slow connection of one user, but will pay off in the future when 100 users are online, in which case the simple "LOCK ALL ONE TABLE AND FULL SINGLE REQUEST EACH TIME" SQLite procedure will start the server.
SQLite is designed for simplicity and stand-alone database applications.
If you expect to have 10 simultaneous writes to the database at the same time, SQLite may work well, but you do not want 100 user applications to write and read data to the database continuously using SQLite. It was not designed for such a scenario, and it will destroy resources.
Given your TeamSpeak script, you'll probably be fine with SQLite, even for some companies this is fine, some websites need databases that will only be read if new content is added.
For this use, SQLite is a cheap, easy-to-implement, self-contained, ideal solution that does the job.