does the structure「(verb stem)がする」 exist?

「臭う」 and 「臭いがする」 have the same meaning, but can this be generalize?

according to google: 臭いがする (49-m hits); 話しがする (17-m hits); 笑いがする (31-m hits); 踊りがする (5-m hits); ...

But, a Japanese scholar told me that, except for 「臭いがする」、"verb stem" + がする is incorrect grammar. I am not convinced. Can someone help me sort this out? To start with, I bet that the verb must be intransitive.

Answer

The word する as a stand-alone verb can be either intransitive as in 変な味がする ("This tastes strange.") or transitive as in 話をする ("to study"), and can also be analyzed as an auxiliary verb that looks like a full-fledged verb as in 日本語を話せはするが上手くない (I speak Japanese a little but not very well). Of course, it can be used with a stem word to form a "X-suru"-type irregular verb (or, more precisely, サ変動詞) as in 取引する ("to make a transaction").

Each class of this verb has various different uses, each of which has multiple sub-categories. Technically, する in 臭いがする is one of the intransitive uses. In a broader sense, this intransitive use appears when the speaker refers to something along the line of a phenomenon, event and symptom. The 臭いがする case falls into one subcategory of this particular intransitive use, where Xがする roughly means "to sense X through a sensory organ." So, X in this subcategory of this particular intransitive use is typically smell, taste, sound, physical feel (felt by your skin), and the like. jlptn1's answer list some typical examples of Ｘがする in this subcategory.

This particular intransitive use has more subcategories. A very common one takes a "symptom" for X, e.g., headache (頭痛がする), dizziness (めまいがする), and tinnitus (耳鳴りがする). Another common subcategory has an "emotion" or "feeling" as X, such as loneliness (寂しい思いがする).

Among many other intransitive uses of する, there is another common one that quite frequently takes the form of Xがする, where it carries the sense that something has a certain quality or property. A typical example would be 見劣りがする (looks inferior/poorer/worse). But this subcategory is further divided into sub-subcategories, one of which uses が before する and the other of which takes の. When to use が and when to use の is well beyond the scope of the question, so I'll stop here.

When する is a transitive verb, X in the form of Xがする must be the doer of the action. So by definition, the verb form of X, if exists, doesn't mean the same thing as Xがする in general.

So, in an intransitive case, X in Xがする may happen to have a verb form as in 臭う for 臭いがする. But this does not mean you can generalize the form of Xがする to other words that have verb versions. If I were asked to give a systematic description of Xがする, it would look like this:

する can be

1. Intransitive verb
   
   
   
   • Usage 1:
     Speaker refers to phenomenon, event, symptom, etc.
     
     
     
     • Subcategory 1:
       Takes form of Xがする,
       X is sensed through sensory organ,
       
       X is smell, taste, sound, feel (felt by your skin), etc.
       Examples: 臭いがする and 味がする.
     
     
     • Subcategory 2:
       Takes form of Xがする,
       X is symptom of some sort,
       Examples: headache (頭痛がする), dizziness (めまいがする), and tinnitus (耳鳴りがする)
     
     
     • Subcategory 3:
       Takes form of Xがする,
       X is emotion or feeling,
       Examples: loneliness (寂しい思いがする) and uneasiness (胸騒ぎがする)
     
     
     
     
     
   
   
   • Usage 2:
     Speaker refers to quality, property, etc.
     
     
     
     • Subcategory:
       Takes form of Xがする or Xのする,
       X is quality, property, etc.
       Example of Xがする case: 見劣りがする (looks inferior/poorer/worse)
       Note: The issue of が vs. の is complicated.
     
     
     
     
     
   
   
   • Many other usages:
     Do not take form of Xがする.
   
   
   
   


2. Transitive verb
   
   
   
   • Many usages:
     Do not take form of Xがする by definition of "transitive verb" unless X is the doer.
     
     Verb form of X, if exists, does not mean Xがする in general.
   
   
   
   


3. Auxiliary verb
   
   
   
   • Many usages:
     Do not take form of Xがする.
   
   
   
   


4. Part of compound verb
   
   　　Do not take form of Xがする by definition.