Implications and benefits of removing NT AUTHORITY\SYSTEM from sysadmin role?
Solution 1:
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.
Solution 2:
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.
Solution 3:
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.