If you do not backup your Master database, then when your SQL Server machine crashes, you would not be able to recover your SQL Server databases.
You should have 2 set of SQL backup jobs. One for those databases with full recovery mode, i.e. they are maintaining transaction logs, and one for those databases with simple recovery mode, i.e. they are not maintaining transaction logs. For the first set of jobs, you must include transaction log backup job so that the transaction logs can be cleared. For the second set of jobs, you should not include a transaction log backup job because there are no transaction logs to be backed up. The Master database should be included in the second set of jobs.
Another thing to note is that you should not change the recovery mode of a SQL database without checking with either the SQL administrator or the database owner. Some application requires a SQL database with full recovery mode and some would specify simple recovery mode.