Having worked on modeling data and sharing results with customers, I agree simpler solutions can be better for ease of explaining alone. Additionally, the loss of x percent accuracy with lower-tech solutions can sometimes be worth it because they are easier to train and reason with. This is particularly the case when you are just looking for loose directional indicators and correlations.
If simple solution gets 77% accuracy, and complex solution yields 80%, I would wager that most of the time you should just stick with the simple solution.
One specific example that comes to mind is in sentiment analysis where you can achieve "sufficiently" high accuracy with well tailored Bayesian approaches. They are super fast to train and reason with. If a customer/consumer wants to know exactly why a piece of text is positive or negative, the n-gram probability matrix is extremely easy to inspect. Subsequent re-training and fixing is also much easier than re-training a large neural network, svm, etc.