At my current job this wouldn’t be much of a problem, since I work in a large convention-style kitchen (at an actual convention facility), and there’s plenty of room.
Most of the restaurant kitchens I’ve worked in, though, have been small enough that having somebody just standing there watching would be a hassle. Restaurant kitchens are [usually] laid out and organized with efficiency in mind, with all of the frequently-used equipment, tools, work surfaces, and supplies within easy reach of the cook. The idea is that a single cook shouldn’t need to be running all over the kitchen to get stuff done — he/she can do everything while standing more or less in one spot.
There’s also the issue of “muscle memory” and "habit’. A professional cook gets used to reaching, turning, and moving in certain patterns, and inserting an extra person into our workspace can end up causing, at best, frustration, and at worst, injury. For example, even in my current spacious kitchen, a constant aggravation is the guy who washes the dishes. He has a tendency to wander into the cooking area for chit-chat and likes to stand close to whoever he’s talking to (standing close is actually a necessity, because the exhaust fans make it hard to hear). But since he’s never actually cooked professionally, he’s unable to correctly anticipate where and when we cooks are going to move, and ends up standing right where we need to be.
Finally, many, if not most restaurants operate on fairly slim margins, and “food cost” is a major consideration. So cooks/chefs aren’t often going to prepare dishes simply for the sake of preparing them, they’re only going to prepare things when they’re ordered by a customer. Even when training an actual new employee, the new guy doesn’t go through training by cooking one of everything on the menu. Rather, they learn the menu by being shown how to do each thing as it’s ordered by customers. And since the customer is waiting, it has to be done quickly. The real learning comes from repetition over time, with an emphasis on “hands on experience”, i.e. doing it yourself. You don’t learn a lot just by watching somebody else doing it once.
Oh, and the “watching” vs. “hands on” part. Unless you’re in possession of a current, valid food handler’s permit, you’re not going to be allowed to actually do anything.