Innovation is interrelated and interdependent
There's a good reason for this thinking - it's very difficult to create something entirely new to an organization that doesn't fit to existing thinking and processes. You either adjust the new idea to existing thinking and processes, or you create new thinking and processes to enable the new ideas. And if you follow that thinking, you can see immediately why firms with highly entrenched methods and processes can find it very difficult to innovate, while firms with flexible thinking and nimble processes and systems can more easily innovate.
So, there really isn't such a concept as "product" innovation as an isolated effort. Creating a new product or service will force you to rethink how you collect and synthesize market insights, how you conceive new products and how you bring them to market. Thinking deeply about a new product or service may in fact lead you to consider new business models or new sources of revenue or new channels as well. This means that what may initially seem like a simple act of creating a new product will in fact force your firm to reconsider how it works. That's another reason why a half-hearted, let's give it a shot innovation programs almost always fail. There are simply too many things that must change to do innovation easily. Yes, you can ramp through a new product or service without changing some of these other features and attributes of your business, but you'll run roughshod over the existing thinking and processes. Not to say they don't need to be roughed up a little, but they'll give as good as they get.
Innovation at any level is interrelated to so many other factors of your business. A new product or service may require a new method to service customers or a new channel, or new business model. New ideas can't live in isolation and may not play nicely with existing ideas - and that's the point. A radically new or different idea needs different organizational structures, channels and models to survive. Innovation is also interdependent with other processes and strategies. Try creating a new innovation effort in your business without communicating what you are doing, or changing how the participants are evaluated or compensated. You'll soon find that while innovation may seem isolated from the "regular" business processes, it relies on and demands services from those processes that may seem unreasonable.
Yes, you can create a skunkworks and hold innovation at arms length. That can create really interesting and radical ideas but will need to duplicate a lot of the capabilities and processes you have already in existence, and the new insights and learnings won't filter back into your existing business. The skunkworks model is effectively like exercising only one arm and hoping the rest of the body benefits. If you plan to innovate, you need to know that you can't simply create a new product. A really interesting new product or service will almost by definition force a rethinking of your existing management styles, business models and org structures.