We say Krishna was an avatar of Vishnu. Why don't we say so many other great saints who preached religion, to be an avatar? Or why don't we consider other great kshatriyas who fought against adharma to be an avatar? How is it decided whether it is an avatar? How is an avatar different from any other soul? A soul is also a part of Parameshwar. So what is the difference between the avatar soul and any other soul?
We say that Krishna was an Avatara of Vishnu because the scriptures tell us that. We would not have known that if it was not mentioned in the scriptures.
So, if some saints are not mentioned as being such in scriptures then we can't really say anything with authority.
Sometimes, however, some of the great saints' biographies claim that they were Avataras of Gods.
For example, Sri Ramakrishna, Chaitanya Maha Prabhu etc are all considered as Avataras. Even Swami Vivekananda is considered as an Avatara of one among the Sapta Rishis. Similarly, many other well known saints are also considered as Avataras of Gods.
As regards the Maha Kshatriyas- i am not sure which Kshatriyas you're talking about here. But if they are the Kshatriyas who fought on Kurukshetra battle, then all of them were Avataras of some deities or the other. Some (who fought for the Kauravas) were even incarnations of the evil forces.
The Devi Bhagavata Purana gives these details:
- Vyâsa said :-- The part incarnations of Suras and Asuras on this earth, and their names I am now saying to you in brief; hear. 30-32. Vâsudeva was the part incarnation of Kas’yapa, Devakî was of Aditi, Baladeva, of Ananta; Vâsudeva S’rî Krisna, of S’rîmân Nârâyana; the son of Dharma existing even at that time in his physical body; Arjuna, of Nara, the younger brother of Nârâyana.
- Yuidhisthira was part incarnate of Dharma, Bhimasena, of Vâyu, the powerful twins of Mâdri, Nakul and Sahadeva, of As’vinî-kumâras?
- The valiant hero Karna, born of Kuntî, was part incarnate of the Sun, and the high minded Vidura, the knower of the Supreme Essence, was incarnate of Yama, the king Dharmarâj. Drona, the Âchârya of the Kurus and the Pândavas was the part incarnate of Brihaspatî; and his son As’vatthâmâ was part incarnate of Rudra Deva.
- S’antanu was the part incarnate of the Ocean; his wife, of the river Ganges in human farm. It is stated in the Purânas that the king Devaka was part incarnate of the Lord of Gandarvas.
36-41. The Grand-father of the Kauravas, the foremost of the heroes, Bhîsma Deva was the incarnate of Vasu; Virâta, the Lord of Matsya was the part incarnate of Maruts; Dhritarâstra, of the Daitya Hamsa, the son of Arista Nemi; Kripa and Krita Varmâ, of Maruts; Duryodhana, of Kali and S’akuni, of Dvâpara; Suvarchâkhya Somapraru, of the son of the Moon; Dhristadyumna was part incarnate of Fire and S’ikhandî of Râksasa; Pradyumna was part incarnate of Sanatkumâra; the king Drupada was part incarnate of Varuna; Draupadî, of Laksmî; Draupadî’s five sons, of Visve-devas; Kuntî was incarnate of Siddhi; Mâdri, of Dhriti; Gândhârî, of Mati; the wives of S’rî Krisna were the heavenly public women; thus all the Devas came as their part incarnations, urged on by Indra. 42-43. Amongst the Asuras, S’is’upâla was the incarnate of Hiranyakas’ipu; Jarâsandha, of Biprachitti, S’alya, of Prahlâda; Kamsa, of Kâlanemi and Kes’î, of Haya S’irâ. The Asura named Arista of the form of a cow that was killed by Krisna was the son of Bali. 44. Dhristaketu was part incarnate of Anuhrâdha, Bhagadatta, of Vâskala; Pralamba, of Lamba; Dhenuka, of Khara.
From Devi Bhagavatam's 4th book's 22nd chapter.
So, the point is, it does not depend on our consideration. We can't decide on our own unless Avatara-hood of some saint is stated specifically in the scriptures or in other important texts.
Now, regarding what are the salient features that the Avatara Purusha must have (so that we can recognize him as an Avatara), i already have a question here.