The relationship between innovation and process
First, let's consider typical innovation in many firms. If innovation is a one-time, discrete event that won't be repeated, there's probably not much need for a defined process, since the work is ad-hoc and can't be well defined, and won't be done again, at least in the short run. In this situation, an innovation process is overkill. We'd argue that many of these efforts won't be successful, since innovation requires skills and disciplines, and risk tolerances that can't be deployed in emergencies or "one time" events.
Now, let's think about innovation as a repeatable capability, a business discipline. If an organization believes that innovation can drive value over time, it would make sense that the organization create structures that allow the effort to be repeated. The firm could define how the work to generate and evaluate ideas should be accomplished - the "work flow" and could begin to define the roles that support that "work flow". If this is beginning to sound a lot like a "process", then you are correct. In a large firm, any work that must be done well is done aligned to a defined process.
A process allows the firm to define upstream and downstream activities, to direct and simplify workflow, assign tasks and responsibilities to people who have been trained in their roles. A process also ensures work is done the same way, within reason, every time it is conducted and that the process and the people involved enjoy the benefits of a learning curve, gaining insights and skills over time. Think about every other important activity in your business. It follows a well defined and well-regulated process, whether that process is a formal, documented ISO certified process or an informal process sustained by the corporate culture. If innovation is important, why wouldn't it have a defined methodology and process?
Many will argue that "processes" can strangle innovation, and to a certain extent I'll agree. In some firms a "process" is built to demonstrate that the firm is engaged in innovation, but the process is meant to slow walk the ideas so the appearance of innovation is projected but nothing is actually delivered. Yes, there are cynical people in some businesses who are interested in the appearance of innovation. In other organizations people lose sight of what is the tool and what is the outcome - the process becomes paramount and ideas stagnate. In other organizations the process for innovation is the same process as is used for other activities, and new ideas don't fit well within the process and are rejected. An annual planning process is a great example. Most initiatives that request funds are highly scripted and based on examples from previous requests, while innovative ideas often don't have the same rigor or documentation, and are rejected. That's not a failure of the process, it's a failure to use the right process or place the ideas into a process meant to encourage ideas.
Yes, I can use process to stymie ideas but most larger firms simply cannot innovate repeatedly without defining a workflow, responsibilities and methods for ideas to transverse the path from idea to commercial product. Let's distinguish between effective processes that accelerate innovation and those failed processes that either weren't meant to accelerate innovation or weren't the right processes for innovative ideas to begin with. Keep the outcome in mind and find the right tools that create the most beneficial outcomes.