The whole concept of loitering interceptors is wrong?
I think that as long as there are enemy airbases with active aircraft, you should dedicate as many aircraft as required to keep those airbases effectively non-operational, even if that comes at the expense of loitering defensive CAP.
If you have loitering interceptors which spend 3 hours on station, you need a total of 8x the number of aircraft.
So a CAP of 6 fighters would need 48 aircraft dedicated to the mission. Plus presumably tankers and AWACs.
But that CAP of 6 fighters could easily be overwhelmed, because your opponent can likely concentrate 12 aircraft at some point during a day, but you don't know when.
Alternatively, with 48 fighters, you could conduct your own mission with 24 strike fighters + 24 air superiority fighters to target an airbase, force an unplanned takeoff of the planes and destroy any left on the ground.
But I do think having a modest number of CAP makes sense in many cases. If you relied on quick-reaction fighters taking off, realistically they won't be able to intercept fighters/bombers/missiles in time.
And when you have concentrations of airbases or rear area airbases with high-value aircraft (eg. bombers/tankers), it is worth have a CAP because their presence will complicate enemy planning. The enemy would have to launch a smaller number of heavy and expensive missiles from a longer distance for example.
If a HQ-16 Battery costs of $60-80Mn and has up to 72 missiles available to launch, the cost of defensive missile salvoes is comparable in cost to the incoming powered missiles (eg. JASSM at $0.8Mn), so it's manageable.
Given the current fleet of approx 550 J-10s, and assuming each performs a 3 hour CAP, that would be more than 60 J-10 on CAP at any time. Yes, China is a big country, but this does seem like enough for a modest border CAP plus some interior CAP.
p.s. main Chinese fighter jet in service was designed specifically with this role in mind.
If we look at the situation 20-30 years ago when it were designed, Chinese doctrine and military capability was very different.
The objectives were much more defensive, partly because of lower military spending and also because they were behind technologically.
But now we can see Chinese doctrine aiming beyond the 1st Island Chain.
Also, a few years ago, Japan could have chosen a neutral position like we see with South Korea today.
But Japan has decided to double down on the US alliance, and the Japanese Home Islands have a lot of runways to host US aircraft.
There are an additional 7 main airbases in Japan, plus the US could potentially stand up 40+ airbases.
So there is a potentially requirement for a lot more Chinese air/missile strikes for these bases.