Coming from Q&A site Stack Overflow, I have some questions for you and thoughts about this that might help frame user engagement or give you some ideas for how to look into the data to understand community members.
What I would encourage is that you think about the people using your Discourse for support and answer some questions about them:
- How objective are the support requests/ questions you typically get? Are solutions generally clear and unambiguous or are they more subjective with subtle differences that benefit from deeper discussion and weighing the costs/benefits of various options?
- How reusable are solutions in your community? Will other members find a solved support request is applicable to their situation?
- What level of expertise does your average topic creator have? Is it likely they feel comfortable asserting that one specific answer is “correct”? Might they be concerned that the solution that worked for them may not work for others
- What level of engagement do topic creators have in your community? Do they come by just to ask their question after being directed there from your company website or do they use the Discourse as a general reference?
In my experience, the value of a solution marker depends on the aspects in the non-exhaustive list above.
The more objective and reusable the request, the more valuable it is to have (and encourage) a clear solution. Subjectivity makes it less likely there is one solution that works for everyone and indicators of a best solution may frustrate people in slightly different situations or who are different people with different needs. Requests that are too specific to the asker may be solvable but the value of having an obvious solution may be reduced if no one else ever has the same issue.
When it comes to the expertise and engagement levels of your average topic creator, low-expertise and less engaged users may not be confident about marking a solution as the correct one or may be unaware of (or never return after getting the solution) the community’s expectations. Particularly with low expertise creators, they may not be able to adequately judge the solutions they get - for example, a proposed solution may technically work but simultaneously introduce security issues that make it a bad solution. How likely this is will depend on the scope of your specific Discourse.
One other aspect that may be worth considering is the format you’re using for these support requests. I can understand wanting the topic creator to indicate an issue is solved particularly in a support-type forum. If the solution is hidden somewhere in the middle of a discussion thread, readers may struggle to find it. The Solved state and its additional quote of the solution directly below the first post in the topic addresses this neatly.
If you’re using the standard Discourse discussion topic format, I’d be curious if that’s an aspect of why people don’t think about marking as solved since (for me, at least) it’s odd to think a discussion can be solved at all.
In May, Discourse officially released the post voting format plugin, which resembles a more traditional Q&A or support format where the initial post is a question or issue and each reply is an answer that may solve the problem. This format moves requests for additional details, supporting comments (e.g. “I have the same issue”), and other interactions to a comment section on the question and answers also get votes and comments to indicate whether the solution worked for them or suggest improvements to the solution.
Votes on answers allow users to quickly find what other community members feel the best solution is since it would be the highest-scoring answer. Assuming you have active members able to vote on the best solutions, this format presents the community-recommended answer at the top, similar to the solved state without the asker needing to do anything extra.
I’d be curious to see whether more people mark Q&A as solved and whether you think this format type would address your concerns.
Whether you use the Q&A format or stick to the classic forum topics, sometimes it’s worth understanding your community to better determine whether your unmet expectations have solutions. If you struggle to retain topic creators as regular visitors, you may not see an uptick in solved status on those topics, even if you send reminders inviting them to return and share any updates with their issue.
Absolutely work towards educating and increasing engagement with your community members but also consider what expectations and goals are appropriate based on the community you have and consider how to address concerns without expecting the users to change their behavior. That way leads to madness! 
You stated in a recent message:
I agree with @Tris20’s take on this but I think it’s worth emphasizing - you seem to be in a spot where you’re looking for ways to adjust user behavior because of your KPIs. Changing user behavior is hard without big changes to the platform that may upset an established core community.
By taking your community’s needs and behavior into account, understanding and being creative with the data you have access to, you can work towards understanding what’s missing. Then you can consider whether there are Discourse implementation changes that will increase community engagement, lead to different behavior patterns, and give you more data to work with. A change could be something small like a custom Like type that indicates “This is correct” or bigger like testing the Q&A topic format, or you may find that you have everything you need already.