There are some very extensive answers on this stretching question on Fitness.SE, which I will use as the basis for this one but adapt in relation to martial arts. Dance, particularly ballet, seems close enough to martial arts due to its large range of motions. Not all martial arts feature extended leg movements, but you can probably infer to some degree how applicable ballet movements are to your martial art given the extremes those dancers can reach.
From a study titled The Impact of Stretching on Sports Injury Risk: A Systematic Review of the Literature,
Ruth Solomon agrees. Professor emeritus at the University of
California, Santa Cruz, Solomon has been a dancer and dance trainer
all of her professional life. She has published dozens of books,
monographs, and journal articles about training and injury prevention,
and is a member of the board of the International Association for
Dance Medicine & Science.
She is often shocked when she walks into dance studios to teach for
the first time and sees dancers stretching on a cold floor.
"I say, 'Please don't do that!' and explain that we'll stretch in the
middle and at the end of class," she said.
According to Solomon, stretching must be an integral part of the
warm-up process.
"As long as the blood is coursing through the body, the oxygen is
flowing through the muscles, and the muscles are warm-then you can
stretch," she said. "But not before. If you don't stretch and
strengthen together, you'll have a weak muscle. The strength must
balance the stretch if you want to control your movements."
Solomon explained that dancers are at risk for injury partly because
dance demands such extended ranges of motion. Moreover, ballet dancers
typically do exercises such as developpes and grand battements that
develop their quadriceps, but may neglect the hamstrings. The
resulting strength imbalance puts extra stress on the knee joint.
"If the muscles are really stretched out, the ligaments may not be
able to protect the joints," she said. "So you get unstable joints,
particularly knees, and you may get hyperextension and ligament
tears."
Proprioceptive neuromuscular facilitation stretches are now favored in
the dance community because they both strengthen and lengthen muscles,
Solomon said.
Rocky Bornstein, a physical therapist and long-time dancer, also
states in the same study:
"Dancers tend to have a lot of laxity in their joints, a lot of range
of motion, so in some cases strengthening may be more of an issue than
stretching," she said. "If you have a joint that is not
biomechanically lined up, the muscles that move it will be working
overtime to compensate. Stretching the muscle without addressing the
joint won't help."
...
"Muscle lengths affect other joints in the body," Bornstein said.
"People with short hamstrings who don't stretch them are going to
break down somewhere else, probably in the lower back. We stretch our
pectorals not just to lengthen them, but to alleviate upper back or
cervical strain. It's allowing joints to move in the best way
possible-and that's not necessarily the joint directly attached to the
muscle."
Another study conducted with soccer players explored the effects of static and dynamic stretching on the hip's range of motion during kicking. The study concludes that there is little difference between prior static stretching and no stretching during the backswing phase (when you get ready to kick). However, dynamic stretching creates a significant difference versus static stretching all throughout a whole soccer kick. Again, the soccer kicking analogue is not a perfect one-to-one mapping to martial arts, but some of the fundamental muscular movements should translate.
One study, titled Effects of Two Modes of Static Stretching on Muscle Strength and Stiffness, compared constant-torque stretching vs constant-angle stretching of the leg flexors on peak torque. The study results show that musculotendinous stiffness decreased after constant-torque static stretching. If the purpose of the stretch is to reduce this stiffness, then constant-torque stretching may be more appropriate than the constant-angle stretching (holding a stretch at a constant muscle length).
Different studies have different conclusions, and there are many variables to consider. It's debatable as you say. In short, static stretching prior to exercise may not prevent injuries. Performing workouts at lower intensities corresponding or relating to the stylistic elements of your martial art is probably better for martial arts than solely stretching. The goal of a warm-up should be to increase the blood flow and temperature in your body, which is not synonymous with stretching (though it can be a component of the warm-up). Your body will adapt to the stress you place on it, and once you have warmed up, then stretching afterwards can help increase your range of motion and relieve muscle soreness.
