Because it's I think way better than the great helmet in terms of sight and ventilation. Then why didn't they continue to use it? Ofcourse then made from steel instead of bronze and from multiple parts to make it cheaper.
It isn't like the Corinthian helmet was replaced by the great helmet; there was a long gap of time between them.
In general, vision, hearing, and ventilation are important considerations when designing helmets. So is, of course, protectiveness. Whether or not, and how, the helmet covers the face, whether with a movable visor or fixed protection, is the place where these considerations meet.
Face protection shouldn't be thought of as independent of the rest of one's armour. How important face protection is depends on the completeness and protectiveness of the rest of the armour. If one is wearing head-to-toe-mail that will keep out most threats on the battlefield, then the face is the single most vulnerable part. Face protection becomes very important. Thus, we can expect to see great helmets and similarly complete helmets most often on soldiers with head-to-toe armour - head, torso, arms and legs all protected. A lightly-armoured infantryman with just helmet and shield would be very unlikely to choose something like a great helm for his helmet - it would restrict vision and breathing a lot, for very little reduction in the chance of being wounded or killed. The benefit would not outweigh the cost. For soldiers who can expect a large faction of their wounds being to their face (because everything else is armoured) can get a large reduction in the chance of being wounded or killed for the same cost in vision and breathing. For them, the benefit outweighs the cost, and the great helmet was used.
As for the Corinthian helmet, it appears to have been largely replaced by more open and better ventilated helmets, accompanied by a shift towards less armour overall - smaller and lighter shields, and greaves being worn less often.
To return to the comparison with the great helmet, something like:
does restrict vision and ventilation. A Corinthian helmet like:
does offer much better vision and ventilation. But it also offers much less protection. If you are interested in keeping spears and arrows out of your eyes and face better, you could wear a Corinthian helmet like:
but this restricts vision and ventilation much more. Not all Corinthian helmets are way better than a great helmet in terms of vision and ventilation.
The problems with the great helmet can be reduced in two ways: first, a movable visor can be used, so that when there is relative safety (i.e., less extreme danger), the visor can be lifted giving excellent vision and ventilation. Second, the eyeslot can be placed closer to the eyes, giving a larger field of view for the same width eyeslot. These can be combined, giving a helmet like:
Rather than an eyeslot, one can even use a perforated visor like:
As the gun started pushing armour off the battlefield, the cost-benefit considerations discussed above suggest that we should see full-face helmets become scarce, and this happened. Partially-armoured soldiers often wore helmets like:
(and, of course, even while fully-armoured soldiers were wearing full-face helmets, partially-armoured soldiers were wearing open-faced helmets like kettle hats and simple iron caps).
We can note two further things. First, a helmet with many elements of the Corinthian helmet returned: the barbuta:
https://commons.wikimedia.org/wiki/File:Barbute_MET_sfsb14.25.579(6-13-07)s1.jpeg
https://commons.wikimedia.org/wiki/File:Barbute_MET_DP-12880-047.jpg
These were a 15th century Italian trend, and don't appear to have been common outside Italy.
Second, full-face helmets (and other helmets with good face protection even if not "full-face") didn't disappear between the Corinthian helmet and the great helmet. This would have been worn by the most fully armoured soldiers. A couple of examples:
https://commons.wikimedia.org/wiki/File:Sutton_Hoo_helmet_2016.png
https://commons.wikimedia.org/wiki/File:Vendel_XIV_helmet_16493.jpg
and other examples would include Steppe helmets with portrait-visors (like the Sutton Hoo helmet above) and Persian and Rus helmets with spectacles and full-face mail protection.