yes, true. But China already have turbofan AWACS KJ-2000 and KJ-3000 very soon
Turboprop is slower but not too slow for First Island Chain, in fact likely a good thing
* Turboprops are far more fuel‑efficient at AEW altitudes, A turboprop burns 30–50% less fuel than a jet at these altitudes
* Turboprops can stay in the air much longer
* They are dramatically cheaper to operate
* Turboprops can operate from shorter runways
* Lower speed = better radar stability
* Turboprops are perfect for “medium AEW” roles
* Turboprops are quieter and cooler (IR signature)
The much longer air time advantage is basically gone as you'll take much longer to get to where ever your patrol area is, not to mention more time wasted means the more crew you need as they'll be exhausted before you even get there.
I'm not sure why slightly lower IR signature even matters when you are a huge transport with a big radar sticking out of it
Better radar stability because of lower speed is one I've literally never heard off as most AEWC aircraft are jet powered and are perfectly fine, can you provide some source for this?
For AEW, you'd typically want to be as high as possible (turboprop lose power and efficiency at high altitude) for a bigger radar horizon unlike ASW where you actually need to be at a very low altitude and where using a turboprop actually makes more sense than a jet.
I don't think a quad turboprop is any cheaper than a jet considering you now have 4 engines to take care of which can be very expensive and probably outweigh the fuel saving. Also a big chunk of cost goes to the maintenance and upgrade of the electronics onboard which exists no matter the platform.
A good chunk of all those advantages you mentioned either doesn't apply or is outweighed by disadvantages. Let's be real the only reason China is using transports for its special mission aircraft is because China has near 0 commercial aviation industry before. There is also a good reason why even European countries with tactical requirements still choose large business jets as the base platform rather than tactical transports.