Increase Max Memory setting on a SQL Server Production
I have a slightly different opinion.

If you are not experiencing memory pressure and your application is just working fine, why introduce an unknown variable (in your case - increasing sql server max memory) ? You have not tested this change, so its a risk.

If you have more bandwidth on your server, you can look into consolidating more instances on your server. 


  Can something suddenly break (or make a performance degradation) if SQL server suddenly has so much more memory to play with ?


Yes, and I faced a perf degradation issue with PROD having more memory and using TF 2335 fixed the issue.

you can read Paul's answer for more details but the gist is :


  The potential size of the buffer pool also affects the optimizer's cost model for data access.