Does it make sense to write user action logs in MongoDB+MySQL?

Question

MySQL

Mixing ODM and ORM

The task is as follows:
We will write logs (user actions), for example, user Vasya deleted 30 contacts or user Misha deleted 50 contacts or something else.

We thought that there is nothing to do with this data in the main database.

Will we get some profit in terms of the speed of writing / receiving data?