There is a pervasive tendency to regard unknowns negatively, as things to be rid of. For a brief sketch of how this bias has hobbled theory and research in areas such as psychology and communication, see the section on negative bias in my chapter in Proctor and Schiebinger's Agnotology book. I also present a summary of counter-arguments to this bias in chapter 2 in Bammer & Smithson (2008). There are some signs of change in psychology; see the 2021 edited book on deliberate ignorance.  One of my PhD students, Will Whitecross, has a neat paper out on how different kinds of curiosity involve different attitudes towards unknowns.  When curiosity takes the form of "interest" these attitudes tend to be positive (e.g., enjoying the pursuit of knowledge or solutions) whereas when it takes the form of "deprivation" the attitudes are more negative (e.g., frustration at not having a solution). 

When unknowns are cast in the form of a social problem or public issue, the usual remedy proposed is education. Although I'm a huge fan of education (I've been in the business for more than 45 years), it is far from being a panacea even for those unknowns that we can and would like to eliminate. I posted a commentary on a paper by Sheldon Ungar (2008) that focuses on this issue.

Given that we can't know any more than a tiny fraction of what there is to know, what else can we do?  One remedy I advocate is knowing how to assess experts and the very concept of expertise. I call this "meta-expertise".