Is it possible for increasing the SQL Server max memory limit to degrade performance? As far as I can tell, raising the SQL Server max memory limit has no drawbacks, provided that sufficient memory is left for the OS and other applications.

Assuming this is the case, can there be any detrimental effects to raising the max memory limit?

The only thing I have seen is this KB article from Microsoft, which states,


  When you configure max server memory sp_configure option in Microsoft SQL Server to a large value, you may notice that a particular query may run slowly. But if you lower the value for this option, the same query may run much faster.


but it only applies to old versions of SQL Server (&lt;=2008).
Generally speaking, no, there is no detrimental effect from maxing out memory once the OS and other applications have been accounted for. This is exemplified through the default settings of SQL Server:


  The default setting for min server memory is 0, and the default setting for max server memory is 2147483647 MB.


SQL Server Memory Configurations (MSDN)

While this setting allows dynamic re-sizing of the memory SQL Server acquires, it also goes to show that there isn't a number that is "too much" (aside from OS/app/version considerations). SQL Server will only use the memory it requires, even though it may reserve more based on the min/max settings. Giving it access to as much as possible simply gives it the room it may need to operate efficiently. 

As Shanky mentioned, in 2012 and onwards, SQL also uses this setting for thread stacks, CLR allocations, and more which may have other effects in specific scenarios when it comes to memory optimization.