Are there nouns in Sanskrit ?

The more I think of etymologies of Sanskrit nouns, the more I get to think that there are no nouns in Sanskrit.

But it is the structural requirement of sentences that subject-words, object-words have to be nouns or pronouns.

So what a word is etymologically and what the word is in a sentence are considerations, which have great influence of the context.

The very first sentence, rather the very first श्लोक in गीता would become a good example. Here is its study. 

In the simple looking phrase of just two words धर्मक्षेत्रे कुरुक्षेत्रे the number of permutations of interpretations can be 
  1. considering धर्मक्षेत्रे as adjective of कुरुक्षेत्रे 
  2. considering कुरुक्षेत्रे as adjective of धर्मक्षेत्रे 
  3. considering both धर्मक्षेत्रे and कुरुक्षेत्रे as nouns.
Interesting it then is, that all of these three interpretations will be grammatically valid. 
By mathematics of permutations, there can be a fourth permutation of considering both धर्मक्षेत्रे कुरुक्षेत्रे to be adjectives. That permutation will not be valid, keeping structural requirement of a sentence. 
By similar considerations in this same श्लोक, there are four words, समवेताः युयुत्सवः मामकाः पाण्डवाः All are in प्रथमा, बहुवचनम्. Hence they are all eligible to be subject-words, subjects of the verb अकुर्वत. We can consider number of sentences possible with as many subject-words =>
  1. धर्मक्षेत्रे कुरुक्षेत्रे समवेताः किमकुर्वत
  2. धर्मक्षेत्रे कुरुक्षेत्रे युयुत्सवः किमकुर्वत
  3. धर्मक्षेत्रे कुरुक्षेत्रे मामकाः किमकुर्वत
  4. धर्मक्षेत्रे कुरुक्षेत्रे पाण्डवाः किमकुर्वत
  5. धर्मक्षेत्रे कुरुक्षेत्रे समवेताः युयुत्सवः किमकुर्वत
  6. धर्मक्षेत्रे कुरुक्षेत्रे समवेताः मामकाः किमकुर्वत
  7. धर्मक्षेत्रे कुरुक्षेत्रे समवेताः पाण्डवाः किमकुर्वत
  8. धर्मक्षेत्रे कुरुक्षेत्रे युयुत्सवः मामकाः किमकुर्वत
  9. धर्मक्षेत्रे कुरुक्षेत्रे युयुत्सवः पाण्डवाः किमकुर्वत
  10. धर्मक्षेत्रे कुरुक्षेत्रे समवेताः युयुत्सवः मामकाः किमकुर्वत
  11. धर्मक्षेत्रे कुरुक्षेत्रे समवेताः युयुत्सवः पाण्डवाः किमकुर्वत
  12. धर्मक्षेत्रे कुरुक्षेत्रे समवेताः युयुत्सवः मामकाः पाण्डवाः च किमकुर्वत
It may be noticed that all the 12 permutations as above are valid sentences. 
But study of the first sentence brings forth that, though समवेताः is etymologically an adjective, it is serving the function of subject-word and hence in the sentence, it should be considered to be a noun. Etymologically समवेताः is क्त-कृदन्तम् of धातुः समवे (सम् + अव + इ) hence definitely an adjective.
One can prove that all the four words समवेताः युयुत्सवः मामकाः पाण्डवाः are adjectives by their etymology. For example पाण्डव (पाण्डोः यः सः पाण्डवः) is basically an adjective and qualifies all five पाण्डवाः. To say पाण्डवः युधिष्ठिरः, पाण्डवः भीमः, पाण्डवः अर्जुनः, पाण्डवः नकुलः, पाण्डवः सहदेवः are all valid phrases, where पाण्डवः is an adjective. 
So, what a word is etymologically and what the role of the word is in a sentence are two different things. Possibly one should be finding good discussion on the role of a word in a sentence in वाक्यपदीयम् of भर्तृहरिः. That could be the logic of its title having the word वाक्य not वाक्. It comes to mind that by this viewpoint, study of वाक्यपदीयम् of भर्तृहरिः has its own significance. Probably such significance of वाक्यपदीयम् has not been brought out at all. There is so much talk of study of अष्टाध्यायी, कौमुदी etc., that study of वाक्यपदीयम् hardly ever gets any mention. 
शुभमस्तु !