I always wondered that as well.
After some scrutiny of Tolkien's original I could now make two different cases, called X and Y:
They will discuss four different claims;
A) Elves of Beleriand did fight together with the Host of the West in the War of Wrath
B) however few of those who fought remained in Middle-earth afterwards [instead of going to Valinor]
C) and of those who stayed none made stories about it that could be a source for those who lived in later days
D) What is actually referred to concern what happend up to the point of the War but NOT the War itself.
Let us go back to the source:
Both case X and case Y hold this true: A is motivated by the section in bright red: Eonwë did actually muster Elves of Beleriand.$15. Of the march of the host of Fionwe to the North little is said in any tale; for in his armies went none of those Elves who had dwelt and suffered in the Hither Lands, and who made the histories of those days that still are known; and tidings of these things they learned long afterward from their kinsfolk, the Lightelves of Valinor. But at the last Fionwe came up out of the West, and the challenge of his trumpets filled the sky; and he summoned unto him all Elves and Men from Hithlum unto the East; and Beleriand was ablaze with the glory of his arms, for the sons of the Gods were young and fair and terrible, and the mountains rang beneath their feet.
- HoME 5; The Conclusion of the Quenta Silmarillion
Case X argues the following:
B and C is covered by the green section. Here the important word is the initial "and". If that implies "all those who fought in the war" instead of "all Elves in Beleriand", the rest of the sentance get a brand new meaning.
It will then just mean that none who fought in the battle created any tales about it or sources for those in later days to work from. We know that many of Elves went to Valinor, so they could not tell about it. While of the rest who stayed no one made any songs or records about it.
Case Y argues the following:
D refers first to the blue parts of the text. Reading it carefully, and considering the chronological order of the blue parts and the red text, it actually says nothing about no Beleriand Elves in the war, but no Beleriand Elves in the march of the Host of the West from Valinor to the Nort [of Middle-earth].
Ergo, the peoples in Middle-earth tell almost nothing about the Valinor host, before it appeared in the North, because they didn't knew knew about it. Why didn't they know? Because none of the Beleriand Elves was in the host in that time, and only those Elves have left records for us (the Vanyar and Noldor of Valinor did not left us sources).
What the Elves of Middle-earth learned about it, the Vanyar and Noldor of the Host of the West later told them (the war raged for 48 years so there was time), but it never became part of any tales; possibly because they knew it only in summarized form or perhaps because it was not first hand accounts.
The Silmarillion text do not give any other impression when this interpetation is in mind, as all points at what occured up till the point of arrival in Middle-earth:
Do not mean that we have better sources for the War, that's sadly lacking none the less, hehe.Of the march of the host of the Valar to the north of Middle-earth little is said in any tale; for among them went none of those Elves who had dwelt and suffered in the Hither Lands, and who made the histories of those days that still are known; and tidings of these things they only learned long afterwards from their kinsfolk in Aman. But at the last the might of Valinor came up out of the West, and the challenge of the trumpets of Eönwë filled the sky; and Beleriand was ablaze with the glory of their arms, for the host of the Valar were arrayed in forms young and fair and terrible, and the mountains rang beneath their feet.
Might forgotten some other part of the textures that contradicts this, but ATM I assign myself to case Y.