I noticed in "Oriental Armour of the Near and Middle East from the Eighth to the Fifteenth Centuries as Shown in Works of Art" by M. Gorelik, in: Islamic Arms and Armour, ed. R Elgood, London 1979; a couple of figures with helmets that are flat on the top: I looked these up in the source given: The Ilkhanid Mongol Kitab-i-Samak 'Iyar, by Sadaqah Ibn Abi al-Qasim Shirazi and found that the flat topped helmets in folio 268b were actually colouring-in over the lines (or smudged). The outline of pointed helmets can be seen. So this isn't evidence for Ilkhanids with flat topped helmets.
The Bodleian Library have changed their online system so I haven't been able to get a bigger detail to check if one helmet has a nasal.
I noticed in "Oriental Armour of the Near and Middle East from the Eighth to the Fifteenth Centuries as Shown in Works of Art" by M. Gorelik, in: <i>Islamic Arms and Armour</i>, ed. R Elgood, London 1979; a couple of figures with helmets that are flat on the top: