A couple of points I'd like to make:
1. If the British switch over to daylight bombing, the Germans wounl't need night fighters. However they would need a lot more interceptors to stop both the RAF Bomber Command and the USAAF, which would both be hitting them during the day. Instead of a single raid of USAAF going for a target in Germany, you would also have RAF raids going for other targets. This will actually put even more pressure on the Germans.
2. The Mosquito RAF bomber attacks would be conducted at low altitude. Therefore you would need a lot less bombs and bombers that you would need in a typical daytime USAAF strike. The Americans regularly used 100+ bombers to hit single targets, like a factory building complex. If you get 30 Mosquitos over the target at low altitude, the target is toast. They will simply hit the damm thing a lot more accurate than the B-17s would.
This also means that the RAF would have the option of hitting multiple targets at the same time, thus putting even more pressure on the Germans to coordinate their defences.
3. Some have pointed out, that the Germans would simply put up more AAA to hit the lot flying Mosquitos and use more fighters. Surely this is correct, but these AAA and fighters would also be a very good target for the RAF. I can imagine Mosquitos being outfitted for the escort role, hitting Germans defences, before the real strike comes in.
4. The Tirpitz is not a problem. Even if the Lancaster is not available, the Royal Navy had the capacity to sink it with a carrier-launched strike in 1944.
5. One problem would be, that you would need a lot more pilots than in OTL. This would mean a larg training project, which could perhaps be partially carried out in the USA?
I like the idea of a Mosquite bomber command and I think it would meet at least the same goals like the original bombing campaign did. The biggest potential is IMHO after 1943, when the Allies dominated the skies over Germany and you have good interceptors (like the P-51) to cover the bomber force all the way to the target.
1000 Mosquitos, each carrying 2 tons of bombs are going to do more damage than 500 Lancaster, each carrying 6 tons of bombs, simply because they are all going to actually hit their targets.