The P-38H didn't have the power the J and L had, because of the intercoolers still being in the leading edges of the outer wings. However, it did outperform the P-38G, and it was the P-38 that both the 55th and 20th Fighter Groups went operational with in late 1943. The P-38H also could not maintain the higher HP level as long as the J and L, as the inefficient intercoolers couldn't prevent detonation for as long as the J and L.
Also, at the time, the fuel available to the 20th and 55th was crap, not only was the octane often way too low, but tetraethyl lead and other compounds mixed into the fuel fell out of suspension, especially in the earlier model intake (the intake on the Allisons in the H and earlier P-38 was not as good a design as the later models) leading to fouled plugs, poor mixture distribution, and widely varying octane.
The theory, so I heard (but NOT from HTC) is that the period between the first P-38 groups going operational, and the delivery of the first P-38J models is short enough that P-38 groups will only be at an artificial disadvantage for a little while. The P-38 groups went operational in October 1943, and the first deliveries of the P-38J to Europe (albeit in very low numbers) came in December. However, the groups' main ride was still the P-38H until well into the early months of 1944.
It would seem that the P-38H would be an easy addition, all you'd need to do is add a little Military power, and add WEP fro a short period, to the current P-38G. Of course, there would also need to be some P-38H skins (I know people waiting to do some P-38H skins though, and there may be a few already done). In all fairness though, the staff at HTC is swamped, and I'm not sure exactly what adding the correct power would entail. Those who argue against the addition of the P-38H (I can so no real reason outside of the HTC workload) say the duration where it is needed is short, and the speed difference is small. However, it is not just speed, it is also climb, acceleration, and energy retention, so they are very wrong. And any disadvantage you shouldn't have is significant.