You can restore each of the system databases to a new installation and you should back them up, so you have all of your instance-level data saved. The only exception is tempdb
which is ephemeral and not meant to be recoverable, since as the name implies, it's meant for temporary storage.
The master
database contains information on all of your Logins and any other system level information. msdb
contains information on all things pertaining to the SQL Agent such as Jobs, Alerts, and Operators and also stores history tables such as mail history, backup and restore history, etc. Finally the model
database rarely changes unless you explicitly customize it, but it is used as the default template when a new user database is created, and having a backup of it can save you from if it gets corrupt (as Tibor mention).
Additionally, if you're using Replication and that server is the Distributor then there's another system database that gets created called distribution
which is used to facilitate its jobs for distributing the changes from the Publisher to the Subscribers. That should also be backed up and can be restored, as well.
Please see Backup & restore: system databases (SQL Server) for more information.
For anecdotal reference, I've been in the situation where my server became corrupt and I had to spin up a new one with a new SQL instance installed, and then restored the system databases too. Quite a relief when you have all the aforementioned instance level data available to you after such an event occurs, and all you need to do is restore the system databases.
master
Database