Every dog and cat I know eats grass. If I were as smart as the creator, knowing there was going to be a time that they needed those teeth and horns, why not prepare them? They won’t need them again once the Messiah returns to rule, so if you survive the tribulation you will get to see. Also, I think when He does rule again and earth is again at peace, lions and lambs, people will live to be 800 years old? I’m going to plant a Sequoia and take a picture of it once a month. The future is my place of peace. Every renaissance of man has been a dark age.
Eat it sure. Can they survive on it? Cats have to turn their heads to eat grass because they don't have flat incisors like horses or cows. Their canines get in the way. They don't have flat molars either, so grinding grass up is extremely difficult. Every time my cat puked up grass the blades were practically whole. All not good for an ostensible herbivore.
Find me the skeleton of a cat with a ruminant's dentition and you'll convince me. Otherwise, that's a mighty transformation to pack into the Fall. I think it's just easier to limit the effect of the Fall to human death rather than animal death.