Do we have evidence it can sustain it vs just reaching it for very short spurts?
Nobody is saying that diesel boats can't go fast. What we are saying is that you need certain power to sustain quick dashes in a carrier group.
Sure, a replenishment ship is unable to sustain the same speed, but it can trail the action. It doesn't need to sprint 6 days from Pearl to 1500 km off Taiwan or sprint 9 days from SCS to Persian Gulf. You need all your escort there to protect your prized carrier. Your primary escort of next 20 years need to be able to carry out all the missions that might come up.
Anyways, you clearly support the idea of CODAD propulsion and I don't. I will just leave it as that.
Diesels can run it as long as they can as long as they have the fuel for it.
It is not necessary for frigates to sprint. The Royal Navy had Type 41 and Type 61 frigates and destroyers that were diesel powered, ran only up to 24 knots, but these were used to radar picket and air defense ships ahead of a carrier group. Decades later after many surface warships in between are consuming expensive high grade fuel, the Royal Navy is going back to all diesels for the Type 31.
Your frigate running at full power sustained to keep up with a sprinting carrier group can find itself running out of fuel quicker before the destroyers did.
Remember that you always have to keep focus on what a frigate should be. It needs to be cheap, reliable, dependable, maintainable, and in the worst case, expendable. It needs to be cheap to operate, and using cheaper diesel fuel aids in the bill. You have a powerplant set up that is already highly trusted, and you already have a base of mechanics ready to fix, engineers to maintain them. You already have your primary escorts with the 052D and 055; you don't need another ship with the cost and mission creep that will eventually compete with them.
If the PLAN wants to go with a one gas turbine, four diesel engine, with electric motor setup, this is an entirely new and untested platform that will necessitate a change of the Type designation, maybe to 057 or 058. They will also build a few ships first, anywhere from two to four, then see how it goes, then fix all the issues for the next batch. Its not something they will build at least eight ships at one time.