Per Ananda (personally I have yet to encounter anyone better informed on Indonesian defence procurement matters who writes in English) the Indonesian Navy is still reluctant to embrace gas turbine propulsion and this is one of the issues with FREMM. 052D/E would not solve this. 052D/E also requires a significantly larger crew than FREMM, Arrowhead 140 or 054A and this is a major contributor to total lifecycle cost.
If Jakarta is willing to entertain Chinese solutions for major acquisition programs such as this, that is much more important than which specific platform they might end up purchasing. That political background is what I would like to read more about.