I think your thought experiment is 2000 fighters meeting an air born threat anywhere in Germany. 2000 fighters alone could not protect Germany. From the UK the USAF could attack from the North Sea and across France from Italy and North Africa they could attack all of South Germany France and Eastern Europe. To protect Germany from all possible avenues of attack would require more than 10,000 aircraft. To take a break to build up such a force would mean Germany did not have any industry or cities in place. I base this on the difficulty the UK had in repelling the luftwaffe in 1940.Their job was to kill the Luftwaffe, the bombers were really just bait to bring them up. That was the great innovation by the great (and always underestimated) Doolittle.
He realised that just chasing them away was pointless, the Luftwaffe pilots lived to fight another day and that would let it steadily build up strength, eventually to level that could overwhelm any escorts.
They had to be killed, chased and killed, setting in train the attrition on pilots and machines that finally killed the organisation.
Take a 'thought experiment'. Say the Luftwaffe had managed to build up to (say) 2,000 fighters over Germany...that would have ended the USAAF's daylight campaign, real fast.
At that sort of numbers they could have (a) intercepted the escorts as they headed towards rendezvousing with the bombers, forcing them to drop tanks and taking them out of the game, (b) staged multi pronged attacks, with enough to draw off the escorts and still enough left to hammer the bombers.
The USAAF then would have had to have built up far greater numbers of escort fighters to counter that (with escorts escorting other escorts at various points).