If a derivative exists the source from which it is derived must also exist. That is simple logic of science. Why are you fictionalising it? Your logic is not logical ..... please comment.
In general, Puranas have a severe distortion of historical facts as these puranas were written at a time of degradation whereby universities like takshashila were ruined and Gurukulas converted yo Buddhist viharas and bhakti tamples. We must take all these later account of puranas (after buddhism got entrenched, after 1AD) with a pinch of salt.
Parashuram is mentioned in Mahabharata and Ramayana very clearly. There are his attributes shown like he refusing to teach kshatriyas and Karna duping him to be a Brahman, he fighting Bhishma to protect the honour of the woman whom he kidnapped but refused to marry.
The later purana retards just wrote anything and everything, mixing up names of kings, inventing new names based upon their understanding of its literal meaning rather than real life name and so on. Puranas and bhakti retards are just low IQ people who unfortunately became Brahmans due to system being degraded to hereditary fashion. These people write extremely ridiculous things which made no sense and had no factual consistency.
So, as far as original sources of Ramayana, Mahabharata and the importance of Parashuram in terms of names given to places (Parashuram kund) and considering Parashuram as 6th Avatar of Vishnu, it makes lot of sense to say that Parashuram was an important figure in history.
Most important point of Parashuram being a slayer or controller of kings (as shown in Mahabharata), makes it appear that Parashuram could actually have been in a position higher than kings in the society and could actually be real head of society. It also confirm with Vedic thought of Brahmans being the supreme Varna and above Kshatriyas. If Brahmans had to live under Kshatriyas commands and Kshatriyas "Alms and gifts", Brahmans could have never been above Kshatriyas. The Parashuram fits in here to show how Brahmans were the real rulers and hence maintained the Vedic thought of Brahman supremacy. Similar analogy of Pope in medieval world commanding Christianity also offers an explanation of how the clergy can dominate the nobility, giving further credence to the idea of Parashuram