Day lilies are perennial, yes but they are not A perennial. The group of plants called Perennials are grouping plants that share the same root structure. That's like Mums and montauk daisies.
Daylilies are actually in the bulb group. Each Daylily is its own independent bulb.
Now, bulbs also can benefit from being split by giving them more room to divide and grow nice big healthy bulbs, but Daylilies in my experience don't need this treatment. They are very prolific and will spread with decent swiftness on their own and may even become a pesky weed if you let them get out of control.
Something interesting about Daylilies is that the bulbs are edible and a viable and sustainable food source. If you have enough of them you can supplement your food root supplies with the bulbs. The bulb itself is interesting, looking kinda like a snail shell in so far as its pattern of growth. It tastes like a nutty flavored onion.
Another interesting edible, which has a lot of flavor variety between strains is the dahlia which is similar to a sweet potatoe but with varying flavor.