Muscle memory can certainly be useful but writing them down again and again is really time-consuming and can lead to burnout. Is there any scientific study which supports that method over learning radicals?
No... the reverse is actually true. Writing by hand strengthens your memory quite a lot as seen in my other answer related to this. Lots of articles and studies have proven that writing things out by hand is generally useful including beating online techniques. Note that all sources and quotes below this sentence are from my linked answer.
Neuroscientists have found that allowing participants to trace out the letters with their fingers, it often works:
Some neuroscientists are not so sure. They think that giving up handwriting will affect how future generations learn to read. “Drawing each letter by hand substantially improves subsequent recognition,” Gentaz explains.
Drawing each letter by hand improves our grasp of the alphabet because we really have a “body memory”, Gentaz adds. “Some people have difficulty reading again after a stroke. To help them remember the alphabet again, we ask them to trace the letters with their finger. Often it works, the gesture restoring the memory.”
So writing can help put memories into your memories very fast, and maybe be even faster than other methods (may beat computerized learning methods). Another source says:
When writing by hand, our brain receives feedback from our motor actions, together with the sensation of touching a pencil and paper.
This only strengthens the fact that writing letters by hand is effective. Your brain takes in feedback from your hands writing out the letters along with the touch of paper and pencil. This helps with your muscle memory. And it's not just muscle memory that's involved here:
When writing by hand, the movements involved leave a motor memory in the sensorimotor part of the brain, which helps us recognize letters. This implies a connection between reading and writing, and suggests that the sensorimotor system plays a role in the process of visual recognition during reading, Mangen explains.
With the feedback/memory stored in your brain, you can actually be able to recognize and write down letters better. Thus there are studies that definitely support writing down letters over other methods.
Of course, there are other methods though: