People in Hawaii keep their Emerald as low as 1/4". Those lawns never need dethatching. Those lawns are also not watered much, if at all and are not fertilized. Grass looks like it is almost dead, but it is not. I have come to really dislike most varieties of zoysia. Only way to make them look good is lots of water and fertilizer. Doing that gives you a thatch problem unless you mow really low very often.
They who can give up essential liberty to obtain a little temporary safety, deserve neither liberty nor safety.
Benjamin Franklin 1775
Sell not virtue to purchase wealth, nor Liberty to purchase power.
Benjamin Franklin Poor Richard's Almanac1738