I understand what you're saying about the tension. As someone trained in psychology, there's a litany of papers that 'solve the problem of not understanding' with little or no 'problem solving' benefit.
Having said that, I think those incentives are changing. In the UK and Australia, universities are now being evaluated and incentivised based on how well they solve problems (e.g. https://www.arc.gov.au/engagement-and-impact-assessment). I think, in general, your motivation and career would not be hurt by doing things that focus on engagement with people who have important problems, and helping to impact their decision-making. Personally, I think even the best 'solve the problem of not understanding' questions start with a problem in real life. I think medicine is a good example of where academic success is often directly correlated with how well your research either solves important problems or has promise to solve problems.
As a fledgling economist, however, I do see you point. There are strong incentives in some fields to come up with some new theory than to solve some existing problem. I guess this is true in medicine too, where there's more money on research for male pattern baldness than malaria (https://www.independent.co.uk/news/world/americas/bill-gates-why-do-we-care-more-about-baldness-malaria-8536988.html).
Still, I never dissuade my students from trying to solve important problems. Even if one of their studeis is something more 'theoretical', I try to ensure they're working backwards from the important problem that's worth solving. To your use example above, even if you do come up with a more general theory of philanthropic portfolio management, you'd hope that your intro and discussion could still speak to how it helps someone answer the policy question: "How much money should I allocate to x vs. y?"
One thing I'd point out is that there are many areas where solving problems does also lead to academic success. Systematic reviews are cited to the hilt because they try to solve an important problem ("what works?"). Knowledge translation is a whole field of taking stuff trapped in universities and getting it out into practice to solve problems. Very very few interventions do economic analyses of their cost-benefit, and those that do often struggle to put a dollar value on the benefit. For example, in this study, we could calculate the cost per bit of childhood cardiovascular health, but couldn't put a dollar value on the bit of cardiovascular health: https://jamanetwork.com/journals/jamapediatrics/article-abstract/2779446 One of my deepest regrets was trying to focus my PhD on something that was theoretically interesting but practically far from helping the most disadvantaged (i.e., do you need to control or accept your emotions to perform under pressure?). I did this because I thought that was what you were 'supposed' to do, and because I thought it was interesting. If I had my time over, I would have started with a bigger problem then worked backwards to find the something interesting and 'at the frontier of knowledge.'
"For some projects, a small adjustment could unlock huge academic value." Would you be able to provide examples please?
I should clarify - I don't mean a small amount of work, but a small conceptual adjustment. The example I give in the post is to adjust from fully addressing a specific application to partially addressing a more general question. And to do so in a way that is hopefully intellectually stimulating to other researchers.
In my own work, using a consumer intertemporal optimisation model, I've tried to calculate the optimal amount for humanity to spend now on mitigating existential risk. That is the sort of problem-solving question I'm talking about. A couple of possible ways forward for me: include multiple countries and explore the interactions between x-risk mitigation and global public good provision; or use the setting of existential risk to learn more about a particular type of utility function which someone pointed me to for that purpose.