I hope you can see from my reply to Phillip that there are different phases during gout recovery. Because, until you reach the maintenance phase, you need to manage gout differently.
So, your rheumy is right to recommend you avoid inflammation triggers. Because you are at risk of gout flares until most old uric acid crystals have dissolved. Also, science now tells us that the complex processes that trigger gout flares are often related to inflammatory foods. But this often has a genetic component. So the trigger could be sugar for one person, fatty acid imbalance for another, or both to varying degrees.
Once you reach the gout maintenance phase, you can often relax diet restrictions. But always try to keep diet generally healthy – or else you just replace one disease with another.