While I agree human go overboard on memory - but many of us are sentient. You kind of need a memory to have the perspective to apply large concepts. I'm glad we do, or we couldn't speak, learn, or an enjoy a good well developed story.
But even simple animals and insects seem to have memory. When bees do that dance to tell them where the flowers are they need a memory to know where to go. Some worms can learn. You need it to learn anything - language, structured thinking, not to touch hot things, without it an organism is basically an amoeba.
Without it everything all just stimulus then response. When one gets beyond a rather basic animal it becomes crucial for survival. In evolution it would give your offspring an important advantage over others.