Because it didn't work.
Passing a type test may mean an engine is ready for production or it may not. I don't know about German engines but the Allison passed a type test in 1937, in 1940 the engines had to be de-rated to a lower power than the type test engine and reworked to bring them up to par, The Sabre passed a type test well before 1940 as did the Vulture and even the Centaurus passed a type test in 1940 or before.
They built around 270-280 JU 222s and yet fewer than a dozen airframes ever flew with them, and those had constant trouble. Using those engines in combat planes without additional work may have been a bigger fiasco than the initial DB 606 deployment.
A type test is only a milestone, however it indicates considerable promise and that the fundementals are OK. A 100 hour type test suggests about a 25 hour MTBO if experience of the BMW 801, Sabre and PW 2800 are considered. If the Jumo 222 passed a 2000hp/100 hour type test in April 1941 it would reaonably capable of producing that level of power in field conditions about 1 year later perhaps 1.5 years latter to give time to freeze the design for production. The problem form the Jumo was the demand for 2500hp takeoff, which just to hard, and the huge amount of time wasted in converting it from aq 45 Litre engine to a 55 Litere engine in order to make the power in a crude simple way.
The othe problem is that it only had one airframe as customer: the Ju 288. When the airframe was decoupled from the engine (it was to utilise the DB610) the engine had no customer anymore.
Look at napier's faulty Sabre; the company wasn't making a competitive engine so it production potential was being underutilised The Typhoon, a simple fighter rathyer than a complicated bomber needed a powerfull engine to be a viable and to compete with the potent FW 190 which created a crisis in the RAF. Hawkers was making Hurricane's, a seriously outmoded product that needed to be replaced by something better like the Typhoon.
The Jum0 222 doesn't seem to have been particularly troublesome: the DB610 howerver was in comparison to the test program.
Hence it just make sense to utilise the Napier product in a new Hawker airframe. Napier's production potential was being underutlised whereas Hawker Hurrican desperately neede replacement.
The Luftwaffe had by then the BMW 801 working quite well, they were usable in the Ju 88 and FW 190. No airframe had been prepared for the Jumo 222.
If fitted to upgraded versions of the Ju 88 family it would have made a very potent fast bomber. It was in fact scheduled for the Ju 388, with speeds of 440mph expected for the two stage supercharger versions.