In short, is it recommended to always activate the Arithabort in SQL
Server?
Yes. Per the documentation:
Always set ARITHABORT to ON in your logon sessions. Setting ARITHABORT
to OFF can negatively impact query optimization, leading to
performance issues.
Furthermore, the option must be ON to use features like indexes on computed columns, indexed views, filtered indexes, etc.
You don't necessarily need to set ARITHABORT ON
explicitly or with instance-wide configuration because modern client APIs set ANSI WARNINGS ON
by default so it will already be set implicitly for databases in 90 (SQL Server 2005) or later compatibility mode. Note that SQL Server 2008 was the last version to support compatibility level 80. Also from the doc:
When ANSI_WARNINGS has a value of ON and the database compatibility
level is set to 90 or higher then ARITHABORT is implicitly ON
regardless of its value setting. If the database compatibility level
is set to 80 or earlier, the ARITHABORT option must be explicitly set
to ON.