Running a hybrid fantasy/tactical campaign where this is a real issue, I have to say that if the rule is going to apply, it's far more important for the cav units who aren't PCs than for the PCs themselves. And if you want plausibility, then the STR score doesn't factor into it nearly as much as raw velocity. F = V * M. It's the size & speed of the horse which is punishing the rider, and in D&D that counts as a STR check.
You may consider, instead of just using the STR score, calculating the Size in as well. Horses are ... Large creatures? You could conceivably add a bonus for that as well which may resolve your issue.