As a Business Analyst, I have a biased perspective.
There are three areas of the business analyst role that are ideally suited to innovation
Understanding domains and business problems
A business analyst brings the experience of learning many different domains and many different problems for domains. That experience brings the understanding that there are similarities between similar problems in different domains.
A business analyst brings a set of tools for documenting requirements, information architecture, enterprise architecture that help solidify the understanding of a domain.
Focus on value
As a change agent, a business analyst focuses on the value of the outcome during an engagement. After having an understanding of a domain, the role of a business analyst is to figure out how to create value for the domain whether this is a new application, a change in the business process, or a more general change. The focus is always on the value the change will make. Understanding that value is supported by understanding the domain and what is valuable in the context of the domain,
Focus on problem-solving.
A key component of a business analyst is solving problems. Whether this is getting to the root cause of an issue, reengineering a business process, or designing an effective application. Critical thinking skills are key for a business analyst to solve problems.
All three areas are exactly the same areas that are required for innovation.