actually, no, they don’t. It’s just that they are most often built that way.
The feed impedance of the DL6WU design is 50 ohms, and many builders prefer to make the driven element a folded dipole, which multiplies the impedance by 4, then they use a half wave coax balun to bring the impedance back to 50 ohms unbalanced.
Other builders of the DL6WU design feed the driven element directly with 50 ohm coax and use a choke on the feedline near the connection to the driven element.
I have used both styles of feed. The antennas used by the VK9NA dxpedition in 2011 were all built by Rex VK7MO using the DL6WU design and fed direct with a choke made from multiple toroid cores. And we worked about 130 stations on EME using that antenna, you can be assured it works well.
Just like the cheap yagis by Kent WA5VJB, it is a direct 50 ohm feed but a choke on the feedline is a good precaution against current on the outside of the coax interfering with the pattern of the yagi.