Yeah, absolutely not. It's not just "a burr hole" and then stick the metal pointy thing in the brain. It is an actual surgery and there are so many things that can go wrong if not performed by someone with actual surgical training.
First, the trajectory itself: you have to know how to use the stereotactic frame in conjunction with the guidance software and appropriately identify your targets, calculate your trajectories, and then match that up with the computer generated ones. You have to choose the appropriate entry site and make sure you're not going to hit anything important. You need to know where you are in relation to motor strip, sensory cortex, the sinuses, and use pre-op imaging to identify any cortical vessels so you can ensure you aren't going to snag one on your way down. Could this part be theoretically done by someone without surgical training? Sure. But as so much of neurosurgery deals with the method of approach, neurosurgeons are best equipped to make these decisions.
Second, complications that may arise during the surgery itself. What if you clip a vessel and have an ICH? Who is going to throw the EVD in or (god forbid) convert to an open crani and know how to manage that in the immediate setting? What if you have a lot of scalp bleeding during your initial incision? You need someone who's facile with a bipolar so that they can achieve hemostasis without destroying viable skin and making the wound close improperly (which is a HUGE deal for implantation surgeries as I'll detail below). What about when you're tunneling the extension wires from the head to the chest? A neurosurgeon will have done this countless times for things like shunt tubing. They'll know to go underneath the galea to prevent erosion and they'll be able to actually identify the galea because they identify (and suture) it in pretty much any of their major cranial procedures. What about if you snag the EJ? A surgeon will know how to identify the abnormal blood and do what is necessary to achieve hemostasis. Closing incisions is also super important for implantation procedures. Is the neurologist going to be able to appropriately place the correct type of sutures in the correct layers to ensure a hemotoma doesn't form, the fascial seal is water-tight, and the skin is appropriately closed so that there isn't an infection (which is one of the worst things that can happen to these patients)? For the surgeon, this becomes second nature and is standard operating (hah) procedure. For the neurologist who has maybe placed a few a-lines during their intern MICU rotation, this is NOT going to be intuitive or easy to master.
And I think most importantly, who is going to manage these patients when they show up in the ED with problems? Infections, exposed hardware, wound dehiscence, all of these are surgical problems and are best managed by surgeons. If you put something into someone, you should be able to manage the complications of that device. One of my least favorite things is when pain management puts a spinal cord stimulator into someone and then declines to deal with it when the patient presents to the ED 3 months later with it dislodged or infected and then neurosurgery gets to take it out and manage the infection and subsequent damage.
My point is that these are not simple things and can't just be thought about in the immediate operative period. There are long term consequences in addition to immediate considerations that require a surgeon to be able to appropriately manage.