I am sorry, but I didn't quite get your question since most of enzymes are proteins. So if you know how to identify an unknown protein what's the difficulty to identify an enzyme that is a protein?
You are right at your end. In fact, the holoenzyme (complete enzyme) is made up of protein and coenzyme/cofactor. The protein part of different enzymes may be similar, but non-protein component may be different. This is a major difficulty. I wonder how can we identify the enzyme if know all the tests for protein identification. May be a trial with antibody interaction protocol.
I think you are a bit confused with the similarities and differences of carbohydrates, proteins and lipids and likewise between different enzymes. All these macromolecular groups are similar in some aspects but they are structurally different to some extent leading to functional difference. In these groups of macromolecules the structural differences are neatly set and so it is relatively easy to identify them by using some set procedures. But in case of enzymes, the situation is a bit different. Enzymes are either proteins or some specific polynucleotides exhibiting catalytic activity. That makes all the differences in identification of enzymes by using a single step protocol. The protocols may identify whether it is a carbohydrate, a lipid or a protein but cannot identify whether it has any catalytic activity and the catalytic activity of these macromolecules designated as enzymes are so specific and varied that it is impossible to detect if we do not apply the appropriate substrate. That is the primary reason behind absence of single step protocol to identify enzymes.
All proteins have some similarity in structure but it is the minute differences that makes them functionally different and for enzymes, the function is catalysis but they catalyze different reactions that imparts their real identity.