The main reason the Mosquito did so well was exactly because it wasn't used in greater numbers. The Luftwaffe's interceptor aircraft and tactics evolved to counter the main threat of the slower heavy bombers, where firepower and armor was more important than speed. Had the Mosquito been the main threat, the Luftwaffe would have evolved differently throughout the war to counter it.
I hear this quite commonly, and it undoubtedly true, to an extent. When the Luftwaffe did develop a group specifically to hunt the wily Mosquito, they performed... not so well. JG300 and NJGr 10, later NJG11, had very little success in actually hitting the Mosquitoes that they were going after.
There was a very good LEMB thread on this about five years ago that I wish I had saved somewhere. The Luftwaffe tried stripped down S/E fighters with radar loitering on likely flight paths - particularly turning areas - souped up twin engine fighters over expected bombing zones and a couple of other tricks.
Yes, had the main threat been the Mosquito, I'm sure that Mossie loss rates would have gone up.
Yes, I'm sure that the Luftwaffe would have developed more effective counters if they'd put the resources into it and they would have devoted proportionally more resources to shooting down Mossies.
If history was different, history would be different...
However, its also my conviction that loss rates never would have been as high as with the four-engine heavies.
I don't think that the Mosquito could, or even should, have replaced four engine bombers though.
I do think that there was a missed opportunity, a very large one at that, to the Mosquito force as a supplement to the heavy bomber arms, particularly the RAF's night bombing force. The 18 months or so that the higher ups in the RAF took to acknowledge the Mosquito's effectiveness was time badly wasted.
In an ideal world for the Mosquito, the RAF would have welcomed the fast bomber idea with open arms, ordered more of them earlier and even pressed for the four-engine powered version that de Haviland kicked around in mid 1941.