Not true and citation needed. Whatever you cite there are competing papers claiming that structured and constrained generation does zero harm to output diversity/creativity (within a schema).

I mean that's too reductionist if you're being exact and not a worry if you're not.

Even asking for JSON (without constrained sampling) sometimes degrades output, but also even the name and order of keys can affect performance or even act as structured thinking.

At the end of the day current models have enough problems with generalization that they should establish a baseline and move from there.