I don’t think your answer is necessarily wrong, however I would view it as in the second example the どんどん is creating more of a build up and a time expression which is making the nuance of てくる make more sense.
They most likely are just looking for you to use the grammar pattern that is being tested specifically. Someone can correct me, but no I don’t think your answer is grammatically wrong, however it does have a different nuance emphasizing the build up and place you’ve now come to of being able to eat it a bit more so than without the てくる
ようになった - The end point has been reached (natto is now edible)
どんどん~ようになってきた - The gradual steps have built up to this point where I can understand Japanese
The どんどん and てくる are emphasizing the coming to the end point, the one with just ようになった is just stating the end point happened.