A problem which crops up over and over in science-art collaboration interviews (and I think this is relevant to any PE projects) is the existence of the more prevalent(?) but less tangible benefits of doing public engagement projects i.e. if a scientist is collaborating with people outside their specialism they don’t necessary have the vocabulary to communicate the benefit of the collaboration. And frequently, especially with art collaboration, this lack of vocabulary results in the collaborators denying the benefits of the engagement to their research.
Others have stated in the past that a public engagement collaboration is like going to see a great film – you don’t always understand how a film has affected your outlook till some time afterwards.
This is why I think a poll like yours is interesting but may not – if the examples are few - represent an accurate picture of the benefits of public engagement to research.