He produced/has produced ten plays

Yes, you can say it. But as in most cases, the likelihood depends on the context.

If the playwright was dead, you would used the past tense.

If the playwright had stopped producing plays years ago and was living with dementia in a care home, you would probably use the past tense, indicating that his career was over.

If the playwright had announced after producing a play that it was his last, you might well use the present perfect to indicate the immediacy.

There is a grey area between the past tense and the present perfect, which means that the choice of tense is dictated by preference and circumstance rather than hard rules.

So it doesn't really help to ask whether you can say it, it's whether in certain contexts people are likely to speak that way. In short, is it idiomatic? And the answer is that it all depends.