Looks like a pretty typical late-medieval/early renaissance close helm, probably early 16th century. The split visor is replaced with a rooster, either for intimidation factor or (more likely) for ceremonial display. The helmet is certainly capable of being taken to war, and during this era, heavy cuirassers would still be wearing similar armor, and the design wouldn't really impede the rider in any way (though it would be a real shame if it got damaged, that's some fine sculpture work in the steel).

Out of curiosity, did you get this picture from the Met? The reflection in the glass looks like an Ottoman armour display I saw there.

Saying 'why' men at arms wore decorated armour is more complicated than it might seem. It is not as simple as 'this simple armour was for protection, this fancy armour was for show'. Many armours that seem extravagant to us were intended for battle. Armour could have both a protective purpose and a symbolic one at the same time.

I would say that this helmet is an armet of the mid-16th century that -could- be worn in combat, but has more extravagant decoration than usual, namely the sculpted cock's head. Its primary purpose was probably not battlefield use. In this case, the cock motif is probably a symbol of virility and aggression. Since the crown of the helmet has a cocks-comb serration on it, the entire helmet was intended to be worn with this visor, as opposed to some other 16th century decorative visors that can be exchanged for a less sculpted alternative. It is likely that the owner of this helmet had another helmet, without the rooster sculptures, that was his primary 'battle' helmet - if he could afford this helmet, he could afford another. It is possible that originally this helmet was associated with a matched set or 'garniture' of different armour pieces, for battle, tournament and parade, that could be 'mixed and matched' as needed for different purposes.

More extravagant sculpted forms like this generally indicate that decoration was the primary purpose of the armour and protection was secondary, rather than the other way around. This sort of embossing tends to capture incoming blows rather than deflecting them, which increases the likelihood that the armour could be defeated - catching a lance on this helmet would also increase the chance of being unhorsed. This helmet's primary purpose is display, but that does not mean it is 'just for show.' Armour both protects the wearer and provides a symbolic representation of the wearer's social position and virtues.

Alan Williams has analyzed a number of helmets like this and found that they are made of hardened steel, fully capable of being used in battle. Just because something is decorated or of fine workmanship does not mean that it is not intended to stand up to battlefield use - representing one's social position properly was nearly as important in battle was as it was in a parade or tournament (among other things, telling people that you are important increases the chances that you will be taken for ransom rather than simply killed). It is better to think of protection and symbolism as two different purposes, where the first is more prominent in some pieces and the second is more prominent in others.

So while this particular armour may have been intended primarily for show, this armour was intended for battle, as were many other gilt, blued, and etched armours of the 16th century. While armour's form followed its funciton, that did not necessarily dictate a simply or 'utilitarian' design.

EDIT - revised for clarity.