Disclaimer: I am not a DBA. I am a database developer.
A DBA just sent a report to our data stewards and is planning to remove the NT AUTHORITY\SYSTEM account from the sysadmin role on a bunch of servers. (The probably violate some audit report they received).
I see a MSKB article that says not to do this.
From what I can tell reading a variety of disparate information on the web, a bunch of special services/operations (Volume Copy, Full Text Indexing, MOM, Windows Update) use this account even when the SQL Server and Agent service etc are all running under dedicated accounts.
If you guys have a change management process in place then challenge this. Make sure that they are aware (they really should be) of it and get their confirmation that this won't affect any services.
If you don't have a change management process to challenge this in then I would at least bring it to them. Hopefully there is a friendly relationship between your developers and administrators where you work and you'll be able to learn something from each other. They may know about the risks and might be able to explain to you why they're doing it and show you how they're doing it in a safe way.
Have these people been asked why they want to remove it, and if they understand what the purpose of the System account is in the first place? I would agree with your guess about an audit report being involved here, and I would also guess that the report just listed which accounts have rights to do what, and that the DBAs are blindly following it by removing any accounts they don't recognise.
Basically the System account is used to give the OS itself rights to Do Stuff. It's not a general user account and shouldn't really be treated as such.
If the DBAs are determined to remove it, maybe try suggesting that they do so on a test system first (preferably one that gets some active day to day use), give it a month to see if anything happens, and then make a final decision.
You didn't say which version, and that's key. If you're talking SQL Server 2000 and Full text is installed, no, you cannot remove it. The reason for that is if Full Text does not run under the local System account, it could potentially throw an Access Violation and crash. And the account Full Text runs under needs sysadmin access to the SQL Server. So there you go.
As of SQL Server 2005 and higher, it depends on what accounts you have your services configured to run under. Here's the Books On-line page with the information on service accounts. Generally speaking, local or domain accounts are preferred over any of the built-in accounts for the major services, thus alleviating this concern.
Setting Up WIndows Service Accounts (SQL Server 2005 Books Online)
One other thing you didn't mention is whether BUILTIN\Administrators have been removed from the sysadmin fixed server role or not. If not, then System still has sysadmin access as it is considered a member of that local security group.
The only legitimate reason for them to do this (and your MS article confirms it), is to try to prevent administrators of the server SQL is running on from having admin access to the databases. The problem they'll have is that any determined administrator of the OS can go back in and add their permission back in because they have full access to the server. It sounds like what they want to do shouldn't negatively affect anything on the DB (unless something is set up to use AD accounts that are local admins and have no specific DB permissions set), but it's definitely something that they should test first like mh suggested.
If you currently have admin access to the DB through being a local admin of the OS, I'd suggest you create a SQL user (or get another AD user account) that has sysadmin access if that is possible. This would ensure you still have access if they make this change.
If the NT AUTHORITY\SYSTEM account has the SysAdmin role in SQL Server, that means that any Windows Service, or Scheduled Task, running under LocalSystem has God-access to your SQL Server. Is that really something you want...??!
Adding to the answer by K.Brian Kelley, from SQL 2012 onwards, both [NT AUTHORITY\SYSTEM] and [BUILTIN\administrators] are no longer given sysadmin by default.
Source: https://social.msdn.microsoft.com/Forums/sqlserver/en-US/94ff47eb-a0e0-4441-9799-b56b5ce3712b/sql-server-2012-ntauthoritysystem-sysadmin-is-not-checked-by-default?forum=sqlsecurity