I don't expect the above is full of truthiness, but it might have been.
I would say Christopher Tolkien only chose another text (dwarf-mask) because he did not have enough actual narrative on the helm to easily incorporate it into a 'finished' tale -- despite that by doing so, when constructing a 'finished' tale at least, he could not represent his father's latest ideas on the matter.
In the Grey Annals (GA) Tolkien penciled in the margin of the entry for 489: 'At once he (Beleg) set forth in search of Túrin [penciled in margin: bearing the Dragon-helm that Túrin had left in Menegroth). But in later writing Tolkien concluded that Túrin left the dragon helm in Dimbar, and Beleg brought it from there to Amon Rudh in the winter. And in GA 495 he also added the note: ['Túrin in the battle wore the Dragon-helm']
So Christopher notes: 'My father must have supposed therefore that Gwindor and Túrin carried it with them after Beleg's death, to Nargothrond.' and further notes a very interesting isolated piece of writing:
'Beleg searching the orc-camp [in Taur-nu-fuin] finds the dragon-helm -- or was it set on Túrin's head in mockery by the orcs that tormented him? Thus it was born away to Nargothrond; but Túrin would not wear it again, lest it reveal him, until the battle of Talath Dirnen.' JRRT
The note continues with the details that Glaurung desired to rid Túrin of the aid and protection of the helm, taunting him, and...
'And indeed so great was the terror of the Dragon that Túrin dared not look straight upon his eye, but had kept the visor of his helmet down, shielding his face, and in his parley had looked no higher than Glaurung's feet. But being thus taunted, in pride and rashness he thrust up the visor and looked Glaurung in the eye.' JRRT
And in GA again, before the doors of Felagund, penciled against a paragraph 'For while he wore the Dragon-helm of Galion he was proof against the glance of Glaurung.'
And from Unfinished Tales: 'Finally there is the suggestion that Túrin was to wear the helm when he slew Glaurung, and would taunt the Dragon at his death with his words at Nargothrond about 'a master of another name'; but there is no indication of how the narrative was to be managed to bring this about.' Christopher Tolkien
So despite these notes the available text to work with was too thin for The Silmarillion or The Children of Húrin ('new' version). Christopher Tolkien explained that for the Silmarillion he had adopted a passage from another text in the 'Narn papers' that told how Túrin found a dwarf-mask in the armories of Nargothrond, and wore it into battle. And though this was written by JRRT it seems, also...
'It seems probable that this story arose at a stage when my father was treating the Dragon-helm as lost and out of the story (from the end of Dor-Cúarthol, the Land of Bow and Helm, when Túrin was taken by the orcs), and I extended Túrin's wearing of it to the battle of Tumhalad.' Christopher Tolkien The Grey Annals
Christopher basically kept the dwarf-mask for The Children of Húrin too of course, again, despite that it did not represent the likely way Tolkien himself would have finished the tale.
'But ^ [?new] Lord gives the dragon-helm to Húrin. His heart is hot against Thingol...'
The space marked by a caret evidently awaited the name of the new Lord of Brethil. Christopher comments: 'In the second appears a new articulation in the unwritten history of the Dragon-helm, together with...'
Sorry, I should have added that earlier.
'... and its wearer warded from wound or death
whoso bore to battle brightly shining
dire dragon-headed its dreadful crest'.
'Lo! we deemed as dead the dragon of the North,
but high o'er the host its head uprises,
its wings are spread! Who has wakened this spirit
and the flame kindled of its fiery jaws?
From The Lay of the Children of Húrin (second version HME III). Also: 'Upon this helm was set in mockery an image of the head of Glómund the Dragon, and oft had Gumlin borne it to victory...' Quenta Silmarillion HME V.
The description (of the Helm) in Unfinished Tales: '... a gilded image of the head of Glaurung the dragon;...'
However: 'Upon its crest was set in defiance a gilded image of Glaurung the dragon; for it...' The Children of Húrin
So the text that Lee illustrated 'allows' for more than the head -- though on the other hand, the head of the dragon could be said to be an image of it, and most of the extant texts (though they vary in date of course) appear to speak to a Dragonhead image.
Some helms from the land of the Angles (England): Sutton Hoo provides one with a visor and a dragon-crest, for example. Another, according to the site at least, is the Benty Grange helmet:
Just a couple interesting primary world examples.
One's hero simply can not declare a time-out in the heat of the battle simply to adjust their headgear.
A helm constructed in the shape of a dragon's head would also be unwieldy in combat, due to the long snout, so just a dragon head casting atop the helm seems in order. Other examples of this would be the helms worn by the Teutonic Knights in Sergei Eisenstein's movie Alexander Nevsky.