I don't think that (sub-word) tokenization is the main difficulty. Not sure which models still fail the "strawberry" test, but I'd bet they can at least spell strawberry if you ask, indicating that breaking the word into letters is not the problem.

The real issue is that you're asking a prediction engine (with no working memory or internal iteration) to solve an algorithmic task. Of course you can prompt it to "think step by step" to get around these limitations, and if necessary suggest an approach (or ask it to think of one?) to help it keep track of it's letter by letter progress through the task.