This is commercial, not research but: A lot of scenarios where explainable AI is needed use simple statistical solutions.

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For example a company I knew had to identify people in poverty in order to distribute a large ($M) grant fund to people in need, and they had only basic data about some relatively unrelated information, like how often these people travelled lets say, their age, etc.

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In order to create an explainable model where factors can be understood by higher ups, and considered for bias easily, they used a k-means approach with just 3 factors.

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It captured close to as much information as deep learning, but with more robustness to data drift, and with clear graphs segmenting the target group and general group. It also reduced use of data, being pro-privacy.

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This 30 line of code solution with a dozen explanatory output graphs about EDA probably got sold for >500k in fees... but they did make the right choices in this circumstance. They saved on a complex ML model, bias/security/privacy/deployment hell, and left a maintainable solution.

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Now for research, it's interesting from the perspective of applied AI (which is arguably still dominantly GOFAI/simple statistics) and communication about AI with the public, although I wouldn't say it's in vogue.