Andrew's book does mention them being used as escort for their bomb laden brethern. It is you that has to re-read the book.
Hungarian production of the 109 was ~3000.
Even using your warped logic, your statement,
"The USAAF made more fighter aircraft in few months than Germans did the entire war" is still BS. It took 4 years of P-51 production to equal Fw190 so called 'fighter' production. So ~48 months(4x12) is only a 'few months'?

Do you even remember what you wrote?
The US-GB should have re-designated their ground attack a/c A-47, A-51, Spitfire Bx etc, etc as well as re-designating the units BSs since all they did was haul bombs, using your logic.
Now tell me how those 4 mentioned, flying Fw190
Fs became aces if they only were used for ground attack. Must have dropped their bombs on their 'kills'.
You should read the account of Buchner (58 total) of
II./SG 2 who flew a pure fighter mission with possible Barkhorn** over Sevasopol. (** the a/c had 2 black chevrons) Then there is Lambert, a
Schlachtflieger pilot who had 116 claims. Not bad for a 'pure' bomber/attack pilot. You still want to claim the F and G were 'pure' bomber/attack a/c?
OBW, I had a cousin check out that 190S. Yes there is a MW50 decal on it but was told that the a/c did not carry or have installed MW50,
ever, as there was no room for it.