I can confirm this is still an issue in releases 1.14.4 and 1.15.2.
I have a world initially created with the vanilla 1.14.4 server jar, and saw this dragon behavior where it flies up and down slowly. After I updated the jar to 1.15.2 vanilla, the dragon's flying patterns remained the same. They dragon does the same things even if you respawn it.
The link below is to a video of me creating a brand new single-player world using the same seed from my multi-player world. As you can see from the title screen and F3 screen, I'm using vanilla 1.15.2. I'm not doing anything special - just getting to the End and watching the dragon fly around.
My computer is running Windows 10 Pro
The expected behavior is a faster change to vertical movement. If you fought the dragon in 1.13 and earlier, the dragon would dive straight down to the central perch, maybe turning once after it reached the perch. In my video, you can see it keeps turning back and forth while it slowly descends to the perch (@ the 3:05 mark). This is because it keeps flying forward, doesn't drop fast enough, and has to turn around to stay above the perch.
For reference, you could see any Youtube video of the ender dragon fight from 2+ years ago - like this one: https://youtu.be/HOYKXVRRV-I?t=1367
I followed the same steps from my video, but in 1.16.4, and can confirm the dragon still changes its height slowly.