What if, instead of adopting the ME262, the German Luftwaffe had issued, in late 1942, a requirement similar to the OTL directive which eventually lead to the development of the
HE162 Volksjager jet fighter? Let's assume the directive is issued in September 1942, and a near duplicate of the OTL fighter is designed, tested, and in production by mid-summer 1943 (a longer period than the OTL Volksjager, to allow for the design issues which afflicted the OTL aircraft to be worked out).
The Luftwaffe also decides to phase out production of ME109s and FW190s by the end of 1943 to concentrate solely on production of this aircraft.
This aircraft could have been produced very cheaply in very large numbers, and would have been the fastest fighter in the air, bar none (it was faster even than the OTL ME262). So by early 1944 the allies are facing roughly twice the number of Luftwaffe fighters (both jet and piston) which existed in OTL, and they are almost all Volksjagers.
How would this have affected the air war in Europe?