For most applications, the difference between read-only SQL injection and read-write SQL injection is minuscule. Your database will typically have all the secrets that an attacker wants to steal, so being able to read those secrets out of the database is enough to be game over.
Having separate readers and writers will double the number of active database connections from your application. This may increase your risk of denial-of-service (DoS) attack. Furthermore, it also makes the application logic more verbose than it needs to be.
If you're worried about the impact of SQL injection, just use prepared statements. And make sure you're really using prepared statements, not "emulated prepared statements". See ircmaxell's answer here for why emulated prepared statements are evil.