You didn't get good answers so I'll explain.

First, an LLM can easily write a program to calculate the number of rs. If you ask an LLM to do this, you will get the code back.

But the website ChatGPT.com has no way of executing this code, even if it was generated.

The second explanation is how LLMs work. They work on the word (technically token, but think word) level. They don't see letters. The AI behind it literally can only see words. The way it generates output is it starts typing words, and then guesses what word is most likely to come next. So it literally does not know how many rs are in strawberry. The impressive part is how good this "guessing what word comes next" is at answering more complex questions.

It doesn't know things.

It's a statistical model. It cannot synthesize information or problem solve, only show you a rough average of it's library of inputs graphed by proximity to your input.

The LLM isn't aware of its own limitations in this regard. The specific problem of getting an LLM to know what characters a token comprises has not been the focus of training. It's a totally different kind of error than other hallucinations, it's almost entirely orthogonal, but other hallucinations are much more important to solve, whereas being able to count the number of letters in a word or add numbers together is not very important, since as you point out, there are already programs that can do that.

At the moment, you can compare this perhaps to the Paris in the the Spring illusion. Why don't people know to double-check the number of 'the's in a sentence? They could just use their fingers to block out adjacent words and read each word in isolation. They must be idiots and we shouldn't trust humans in any domain.