The phrase "a productive writer" is correct and usable in written English.
You can use it to describe someone who consistently produces a significant amount of written work or achieves their writing goals effectively.
Example: "As a productive writer, she completes several articles each week while maintaining high quality."
Alternatives: "an efficient writer" or "a prolific writer."
The first thing you need to become a productive writer is self-discipline.
During his year abroad, Gidwitz says, he developed the self-discipline necessary to become a productive writer.
I soon discovered that Bird, a nineteenth-century expert in hymnology and hymnody, in other words, the study and performance of hymns, was a productive writer.
The Woolf that Professor Marcus knows and loves is funny, witty and clever, a committed feminist and pacifist, a productive writer and editor.
Crampton Brophy appeared to be a productive writer, having published at least seven novels that mostly focused on secret relationships between, as she put it, "rugged men and strong women". The lead male characters were almost always Navy SEALs.
However that may be, from Proclus' extant works and the information about his lost works it emerges that he was a productive writer indeed.
A moderately productive writer can be a good parent and a good tennis player; someone who feels the need to churn out several best sellers a year probably cannot.
Being an exceptionally productive writer, he composed commentaries on Aristotle, Euclid and Plato, systematic treatises in all disciplines of philosophy as it was at that time (metaphysics and theology, physics, astronomy, mathematics, ethics) and exegetical works on traditions of religious wisdom (Orphism and Chaldaean Oracles).
Still, he was a very good (and incredibly productive) writer.
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